Tablets always turned on (usb-powered). Problems? I need to install about 20 tablets powered 24/7 (24 hours, all week). Is there any problem or potencial damage about it?
There should be nothing to stop you from doing so.
As long as you keep an eye on those tablets and make sure they are setup as they are supposed to they will work.

Small suggestion: Don't connect them 24/7 to the charger. The battery will wear out slower if you keep it's charge between 40-80%.
Android shouldn't be a problem for you.