Either your opponent will have to lose life or you will have to gain life to start the process. Then, yes, unless someone does something to stop it, you'll enter a loop which will win you the game.
Actually, you will not win. According to the comprehensive rules on infinite loops, if a loop contains only mandatory effects, the game ends in a draw. Since the cards don't say may, they are mandatory. Sorry no game winning combo here.
the combo one goes till the opponent is at 0 life it is not infinite. The life has to come from somewhere if no opponent has life/ they are at 0 life the the combo ends. And the hex proof/ platinum angel thing do stop the combo but not in a draw. The opponent will be at zero, just not dead.
In the comprehensive rules for Magic, provided by Wizards of the Coast, they have a rule specifically for this. Loops that players enter that can be broken by way of countering it or changing a condition, can result in the creator of the loop winning. If there is no possible way to counter the loop, break it or change a specific condition about the loop, the game is considered a draw because there is no way to counter.
[[Rule as seen in the Comprehensive Guide found at http://www.wizards.com/magic/comprules/MagicCompRules090201.pdf]]
Direct Quote for Rule #102.4b: "If the game somehow enters a “loop,” repeating a sequence of events with no way to stop, the game is a draw. Loops that contain an optional action don’t result in a draw."
What this means is that for such a combo as Exquisite Blood and Sanguine Bond, when the second card in the stack is allowed to resolve, causing the first to trigger and so on, creating the loop, at any point, the opposite player is able to counter it. Before, during or after the loop initiates, the opponent can use any number of cards to create a condition or remove or counter one of the cards to end the loop, or prevent it in such a way that it ceases functioning or works differently.
This means that even if the opponent is running a pure Aggro deck and runs no counter cards whatsoever, technically, they have the ability available to them to try and counter or change a condition. Because they could have had a card to do so, the loop is legal and if allowed to continue, will allow the one who initiated it to win.
Now. If it at any point the loop becomes impossible stop, meaning that if at any point, even if the player has counter cards available to use but still cannot stop it in any fashion or change conditions in the loop, this would be considered an illegal loop and would result in a draw for the end of the game.
So for example, if I have such a card active that prevents the opponent from attempting to counter, remove, exile or otherwise do something to the cards in the stack, which would cause the end of the loop, or create a condition in the loop to stop it or change what happens, it is an illegal loop because I am now taking away any available options.
This kind of situation has happened plenty of times before and what it boils down to is that it is not the loop-holder's responsibility to make sure the opponent has the cards available to counter it. The two cards for the original stack are easily able to be countered as they are alone. It is the opponent's loss for not having a card available to them to do something to the loop. They have the ability to still counter one or both, if they could. Being able to counter the cards is not dependant on what cards you use or what type of deck you run. The moment that power is taken away from you to react to those cards, regardless if you own the cards or not, it becomes illegal.
Think about it this way; you have a door that needs a key. If you have the key, you can open or lock the door, if you don't, you can't but it's not impossible. The option is always there in every circumstance, it only requires a key. Now, say someone takes the only possible key away from you and breaks it. It is now impossible for you to have the power to unlock/lock the door at any time in the future. That is the difference between legal and illegal loops.
To make it even simpler, say, there's a windowless, steel room you can walk in and out of as you please. Whether on the outside or inside, a key is hidden for you to find to lock it closed with you in it or not as you please, the key being hidden away with each use. This is the legal opportunity. Whether in or out of the cell, you have technical access to it.
Now, someone comes along and has stolen away both keys and has locked you in the steel room. You are now trapped with no way to escape. This is the illegal situation, where you have no possible means or options available to you to escape the cell, thus robbing you of your will.
When the player's will is robbed in this such way during an infinite loop, preventing them from getting out of it or changing the outcome, it is illegal and it is a draw. With only your means of getting out "hidden", or not readily available, it is not illegal because you do have the potential to get out.
Doing this to yourself, you are the one responsible for not finding the key each time to do what you want. Your library is the same way. Your library is the keys to the kingdom and it will be your fault for taking out or replacing different keys. Whether they be keys to the throne room or keys to the toilet. You are responsible for them.
As a side note; It should be noted that doing something like Platinum Angel is a legal change if and only if you're not entering a loop that hinges on her power.
If you normally put yourselves both to zero, gain life and then get rid of Platinum Angel, you win now that the power from her condition is lifted.
If the player initiating the stack of Sanguine Bond and Exquisite Blood does not have an available counter to get rid of or otherwise remove Platinum Angel's condition, either before or during the loop, it becomes illegal because it can now go without end. Platinum Angel keeps the game from ending when it should, thereby causing a truly endless loop to form which can't be stopped.
The players technically have until one or both of them reach zero. If the stack initiator can somehow get rid of Platinum Angel before or after his opponent reaches zero, he can still win by his loop. If he cannot, the game has become a draw because Platinum Angel has effectively made it impossible in this circumstance for either player to win and/or lose.
The reason why Platinum Angel is illegal in this circumstance, and not the stack, is because the Platinum Angel has changed the fundamental laws of the game to the point where the game has become unplayable. Normally, any amount of cards can do this, within the limits provided to them, but as soon as the game has become impossible to proceed with, such in this case as an eternal loop with nothing to counter it, it becomes illegal. The stack at least ends when the opponent reaches zero. Platinum Angel makes it go on and on and on for eternity. This makes it a draw by default.
In a tournament setting, this is also not considered a direct loss for the player with the Platinum Angel. Normally infinite loops keep a game from ever going forward, causing the game to stall out and thus illegal and the person responsible for the stack can be accused of cheating. In the case of the SB and EB stack, it is not eternal until Platinum Angel is in play. In this situation, the player is not stalling the game, he is keeping himself from losing (or winning) at this point. Because neither player can now win, it becomes a draw.