I don't think we understand enough about the dark energy driving inflation to say that. If the force is constant for a given pair of particles at a constant distance, and the atoms are currently stable, that would seem to imply that the force from dark energy pushing the atoms apart will be the same as they are now.

However, as I said, I don't think we know enough about dark energy to say anything about its effects on the atomic scale either now or eons hence.

You're describing the Big Rip. It's now thought that the acceleration of expansion is not high enough for that to happen. Gravity is strong enough that the particles inside galaxy groups will stay causally connected indefinitely. Long enough into the future, whole groups will become disconnected from the rest of the universe, though.