The creator of Dominion has stated that the reason for the first player advantage is that he or she can effectively get more turns. If you force everyone to have the same number of turns using phantom Provinces, then you should nullify the first player advantage.
Getting an extra turn is definitely an advantage. But going first is
only an advantage if you get that turn. If you go first but don't get
an extra turn, a tiebreaker going to the other guy amounts to just
randomly stealing a deserved tie from you. You didn't play worse, you
just randomly went first. A tiebreaker there doesn't solve the problem
of an advantage due to going first (and does nothing for cases with no
tie); it just randomly awards victories in some cases where there was
no such advantage. It's the same as flipping a coin.
So among casual gamers, up until the creator of Dominion, the phantom Province houserule seems like a pretty reasonable fix.
At the "expert" level, as GendoIkari points out, this house rule does no good. Besides the issue of game ending, there are also powerful mega turn decks that get weird. Let's say King's Court, Bridge, and Worker's Village are on the board. You can start to create decks that can buy 20 Provinces in one turn. In these games, the SECOND player gets the advantage. Let's say both players are building power decks, and on a given turn, both P1 and P2 can buy 7 provinces in a turn. If P1 buys 7 provinces, P2 can build for another turn. Now P1 has a stuffed deck, and if he buys 1-2 provinces on the next turn, P2 can pounce and buy 12+ provinces and win. On the other hand, once P1/P2 are able to buy 8 Provinces, if P1 doesn't go out with a bang, P2 will buy out the pile and P1 won't have bought anything.
I would say that if your group (1) doesn't count points so that people know who is in the lead and by how many points, and (2) doesn't produce decks that can buy >2 Provinces per turn, playing with the house rule is more fair than playing without it (of course, playing a bunch of games and exchanging 1st player position is best).