John's probably thinking that if Bob Dylan can win the Nobel prize for Literature, he must be in with a shout for the Science prize.
Whilst he's not renowned for blowing his own trumpet, he is sure he can rely on Annabelle to bum him up and sing his praises to the world at large.
It's possible that the only thing that deters her is her opinion that his ego is already over-inflated, and that this further accolade will make him impossible to live with.

I've no doubt that she will help fight his corner---it remains to be seen, however, whether she will " bum him up " before or after singing his praises.