I have a manual preheat fluorescent desk lamp that takes 2X F15T8 bulbs. The socket is the same, and the fixture looks like it can physically accomidate them, but I am not so sure it can electrically accomidate them. If i were to put F20T12 bulbs in this fixture, what would happen? Nothing, Ballast burnout, Lamp burnout?

Assuming the lamps can physically fit, they would be under driven. The ballast would likely run cooler as well. Other than that, not much.

F20T12 lamps are 24 inches whereas F15T8 lamps are 18 inches. Also, not all T8 fixtures can take T12 lamps.

Side note : I'm currently using European F18T8 lamps which are a drop in replacement for F20T12 in preheat circuits in under cabinet fixtures, but I use appliance F25T12 chokes so they run nice and bright. They heat up the cabinet insides, though (I cannot keep chocolate on the lower shelf above the lights).