Well, I decided to do a little experiment.
Being not too great with maths, I used an online calculator for visual magnitude Vs Absoloute Magnitude Vs Distance (
available here)
And combining what i learned on another thread here; the most luminous known star in the known universe is R136a1 in the LMC (actually, in the tarantula nebula). The Absoloute Mag of this star is supposedly -8.09. At the 50,000 parsecs distance of the LMC, that makes it a 12th VMag star, although if you calculate what it's mag should be using the above calculator, it should actually be 10.4 visually. Maybe there's some intervening gas and dust or something?
Anyway, that same star placed in M31, 780,000 kiloparsecs away would be 16.37 VMag. My scope has a theoretical limit of 15.7, so it seems like there's no way it could resolve stars in M31, even if it was full of R136a1 type monsters.
Hubble (the man, not the telescope) studied cepheid variable stars in M31 to establish that it was an independent galaxy much further away than the foreground stars, but I believe much of his work was photographic in nature. So yes, as was mentioned below, individual stars are possible to see photographically, but not visually - which rather casts into doubt the veracity of the article I mentioned below where there were supposed sightings of stars in the andromeda galaxy with amateur telescopes.
-Markus