I think it is complicated. Will the payment model automatically mean it will fail? No, not all by itself. But, with it being P2P, it has to be better than the competition out there that doesn't charge a monthly fee. So even if it is a great game, but there is another great game(s) that doesn't have a subscription fee, people would be more inclined to play the non subscription game(s) that is just as good. For me personally, ESO will have to beat GW2, and since it does have P2P model, I will not buy the game on day 1 as I originally planned if it was a B2P game. I will wait for player feedback, and more than likely wait for a free trial. When I get to play it, if it does not beat GW2 in enjoyment factor that would make $15 worth it, I will not subscribe, but if it does, I will subscribe and still play both games. If the game was B2P, then it would be likely I would have bought it on day 1, and played both ESO and GW2, spending money on both games, even if ESO is just as good as GW2 or even just a little bit not as good as GW2, but with the P2P model, it has to be GW2. So right now, ESO went from it needs to be good for me to play and spend money, to needing to be better than another game to get me to spend $15 a month on it.
In short, with a P2P model, it is more dependent on the quality of the game and the quality/quantity of new content, where as with B2P people are more likely to be little more tolerant with the game since they do not have to pay $15 a month to play it, or even to come back and try the game to see if anything has changed since they left,