There would be some variance depending on the relationship status after Morrison's run, but I think largely everything stays the same.
House of M/Decimation
Still happen.
Mutants are on the verge of being extinct.
Deadly Genesis
Still happens.
There's nothing Jean could say or do that could smooth out Xavier's 'betrayal'; Scott still kicks him out.
If anything, Jean might leave with Xavier.
Messiah Complex / War / Second Coming
Still happen.
Schism
Still happens.
No matter what, Logan leaves and takes most of the team with him.
I don't think the bro-fight breaks out to that ridiculous scale, but I also don't think Jean would've been able to smooth things out enough so that Scott is welcomed back to Westchester.
Avengers vs X-men
Still happens.
Logan still tattles on Scott to Cap.
Jean would believe her time-traveling son, Nathan, just like Scott did.
Any possible case she would have made to stop the Avengers from storming the beaches of Utopia would've been shut down faster than you could say "Broccoli people".
Rachel was present during that incident and the Phoenix still forwent her for Hope - which tells me that it would've done the same to Jean if she was there.
Everything plays out pretty much exactly the same - the Phoenix still corrupts Scott & the P5, kills Xavier, and is exorcised by Hope.
The only thing that might change is that Jean would be able to advocate for Scott afterwards, so that maaaaaybe he's not a criminal.
Mutant Revolution
Doesn't happen.
Flat out does not happen if Jean were alive. This is, hands down, the one thing that would certifiably be different.