That's right, they use N1-Methylpseudouridine instead of uridine (the nucleoside contained in uracil, which is the U in mRNA sequences) to last a bit longer (but not forever) and to avoid triggering immune reactions to the mRNA itself (the immune system can detect foreign mRNA).

Certainly the vaccine's mRNA sequence breaks down into separate nucleotides. If it did not, continued production of the antigens would cause a chronic immune reaction and/or immune exhaustion that would make the vaccine ineffective.

I don't know what happens to the N1-Methylpseudouridine though. That's an interesting question.