You could... but...
The two channels are out-of-phase. The distort channel has an extra FET stage.
If you could find an effect with the output out-of-phase with the input, then you could use it to place both of the channels back into phase. Something like the old ElectroHarmonix LPB-1 booster would work well.
You could also ignore the out-of-phase channels and find some interesting tonal options by placing one channel on full bass and the other on full treble.
Also keep in mind that the dual inputs for each channel are tone-altering (i.e. one bright, one normal). Not like the dual level inputs that you would find on Fenders and Marshalls. If you normally use the bright input, then you could bridge using the normal inputs of both channels.
