Fabian's answer makes it quite clear that this is not in the rules. For your followup, whether or not this is advantageous, the answer is the ever frustrating "it depends"
Most novice games are decided merely by who makes the biggest blunder first. In that regard this doesn't really do much. In fact, by exposing your line quicker, you might be doing yourself more harm than good.
Once you advance past the novice levels, then this is a huge advantage. White wins between 52% and 56% of the matches, where you would expect 50/50 otherwise. And that's just from being able to move first. Being able to interject a second move would push this even further. Even if black were able to counter with two opening moves of their own, clearly moving first is advantageous, so two first moves would be even more so, especially considering the opening moves for white are very often two pawns anyway.
One plausible way to look at this rule is that perhaps black can move two pawns to try to fight the advantage received from white moving first. But that is pure speculation. The real way to test this counteract this kind of advantage is to play a match and alternate between black and white, or have the losing player be white.