Can you plug an electric guitar (probably Variax 600) into an acoustic guitar amp through a PODX3 Live and get reasonable acoustic and electric guitar sounds?

Generally you can , but that acoustic amp is made for acoustic guitar so the sound range is adapted for that purpose.Same as playing playing guitar/keyboards on a bass amp, you can get some usable sound but it won't sound good as using proper guitar/keyboards amp.

Cool. It's mostly just acting as a stage monitor anyway. The PODX3 will be pipped into the PA.

Well, the best way is to try and see what it will sound like. You will have to tweak the gear to find a proper tone no doubt.

I would try it anyways and hear how it feels. Your ear should always be the most important judge when it comes to sound !