One of my guitar teachers is strictly classical. I know he owns an acoustic amp. Im thinking of buying one of those gretsch hollow-body guitars and lending it to him, will he be able to play it trough the acoustic amp or are there pitfalls?
The main issue with using an electric guitar through an acoustic amp will be the the use of overdrive / distortion pedals, and not the fact that the guitar itself is considered "electric".
The main difference between acoustic and electric speakers is that the acoustic amp will generally have a tweeter to extend the higher ranges and give a more hi-fi like quality - similar to a good PA system.
The problem with overdriven guitar is that it generates many overtones at high frequencies and will sound very harsh through an acoustic amplifier. An electric guitar amp will generally start to roll off at 3kHz, and this removes the extreme high frequency content. Things like the line 6 pod will have a speaker simulator that basically rolls off the highs to allow it to be put directly into PA systems.
However with just a direct guitar it will sound fine - as long as a distortion pedal is not added.
No pitfalls, and actually acoustic amps can make a good match sound wise with archtop/hollow body type of guitar and bring out more of an acoustic qualities of these instruments.
The eq on acoustic amps is slightly different from that on electric guitar amps - and that on bass amps, too. Having said that, any amp will amplify any electric guitar - and obviously, an electro-acoustic guitar is electric!
There should be sufficient tonal control to get a decent sound that way, especially for playing in a studio, and teaching with. At worst, a simple eq pedal will help restore any lost tone, but it should be fine - given that the pitch range of an acoustic guitar is close to that of an electric.
First, find out what your teacher is using as a source - a microphone strapped to his acoustic guitar, a piezo pickup, etc. See if the output impedance and voltage of whatever guitar you're lending to him is directly compatible with the input specs of his amplifier.
It may turn out that a preamp is required to match those parameters. It's rather like the difference between a passive and an active output from a solidbody electric (with mag pickups).