The standard answer I've seen presented for "What is the largest tile possible in 2048?" is 2^17, produced by collapsing a 16 tile long chain into one large tile in the corner.
The answer then generally states that it would be impossible to create a larger tile because it would take a 17 tile chain to create, which is space that we no longer have.
I find this answer compelling, but I have a friend that disagrees and posits that because it takes 15 moves to collapse down to the 2^17th, 15 more tiles are generated, providing the opportunity for them to collapse, giving you a "head start" so to speak toward 2^18.
To be clear: I do not agree with my friend, and don't believe the extra tiles make a difference, but is it possible that it could? If not, is there a simple way to explain why?