I would assume you CAN but why you would I'm not sure.
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It probably won't sound as good as if you had an electric amp, but I don't know it would screw up the amp. Why are you wanting distortion from an acoustic amp?
Telecasters-->Dunlop Volume Pedal-T1M Pearl-AMT Japanese Girl Wah-Line 6 M9-Ibanez DE7-EHX Cathedral-->Mesa Boogie Nomad 4x10 combo
if you put a distortion pedal through it, yes. i have a friend who has an acoustic marshall and he runs some distortion pedal through it and it sounds pretty good. are you playing with an electric guitar? if not, i am not so sure this would work.
my gear: ibanez destroyer( with gibson 500t pickup), epiphone les paul plus,ampeg electric, marshall jcm2000 triple super lead half stack