Yes, you can, for the same reason you can in other formats.
The first Golden Rule:
101.1. Whenever a card’s text directly contradicts these rules, the card takes precedence. The card overrides only the rule that applies to that specific situation. The only exception is that a player can concede the game at any time (see rule 104.3a).
They'd have to ban or restrict the card to limit its use, but it's legal in that format.
Sheldon (EDH Rules Committee) has answered this question directly.
The RC has discussed it and for the time being thinks that multiple Rats is OK. We reserve the right to change our minds down the road.
Although some rules differ from the official MtG rules (i.e. "outside the game" ,Living Wish, is handled differently than other casual formats), Relentless Rats' ability is covered in CR 112.6m. If Relentless Rats were banned in EDH, you couldn't use any copies, but since it isn't you may use any amount from 0-99 copies because [CR 112.6m] specifically allows you to ignore [CR 903.5b].
112.6m An ability that modifies the rules for deck construction functions before the game begins. Such an ability modifies not just the Comprehensive Rules, but also the Magic: The Gathering Tournament Rules and any other documents that set the deck construction rules for a specific Constructed format. However, such an ability can’t affect the format legality of a card, including whether it’s banned or restricted.
903.1. In the Commander variant, each deck is led by a legendary creature designated as that deck’s commander. The Commander variant was created and popularized by fans; an independent rules committee maintains additional resources at http://mtgcommander.net. The Commander variant uses all the normal rules for a Magic game, with the following additions.
903.5b Other than basic lands, each card in a Commander deck must have a different English name.
There's two answers to that question, depending on how you read it.
- Can you put 99 cards named Relentless Rats into a commander deck.
Yes you can, Relentless rats is one of the 16 cards that you can have more than one copy of in your deck (the 11 different basic lands, Relentless Rats, Rat Colony, Shadowborn Apostle, Seven Dwarves, Persistent Petitioner). The rules specify you can have any number of copies of basic lands, and the cards themselves specify you can have any number (or specifically 7 for the dwarves) of the other 5. The very first rule in magic, Rule 101.1, specifies that you follow the card's oracle text when it conflicts with the rules (after all most abilities add to or remove effects of other rules, like Haste removing the effect of summoning sickness).
- Can you play a deck with 99 Relentless Rats.
Nope, the deck is legal, but with 99 Relentless Rats in it, that means you have nothing in the deck except Relentless Rats, there's no way to actually play the deck. If you want to build a deck like that, you probably want to top out at 70 Relentless Rats, if you play nothing but the rats and land.