Admiral Archer is very much alive and well in Trek 11 - no reason he shouldn't be in the Prime universe.
They never said it was Jonathan
Archer. As far as we can tell from the canonical information in the film, it could've been his son or granddaughter.
Not to mention that the Abrams film was set nearly a decade before Prime-timeline TOS. If it were Jonathan, he would've been pretty damn ancient in 2257 (145 years, to be precise, which would be astonishingly old for a human of that generation). His odds of making it to the TOS era proper would be extremely slim.
And for what it's worth, the IaMD bio screen had Archer die in 2245, though I don't think that part was seen on camera.