It would be more like a low wing airplane flying upside down than a trainer flying upside down.

A trainer flying upside is completely unstable in that position. It "wants" to flip over... that's the whole point, actually.

The fuselange of a low wing plane is like an inverted pendulum - it wants to fall over. The wing has dihedral to counter the effect of the inverted pendulum so that the net stability is neutral, or slightly positive. Flip it over (fly it inverted), and you get the trainer with anhedral. Taking the dihedral out of a low wing plan can move it from being nuetrally stable to negatively. Dihedral has to be balanced against other effects.

Here some interesting info on the subject presented by Ed Moorman, who posts here on RCU:
http://members.cox.net/moorman1/ProjectJoss.htm