Yes, it is quite possible (and depending on your device, fairly similar to using it on a laptop). What you will need:
DOSBOX (Google Play Market)
Windows version of ADOM
Once you have installed DOSBOX on your android tablet, you will need to put the ADOM executable inside the directory you designated to be the DOSBOX's file directory. Once you have done so, you simply need run the adom.exe file and you will be playing the fully functional version of ADOM! If you are on a non-physical keyboard device, DOSBOX provides you with a virtual one (it's a bit clunky, but you can get used to it). If you have a physical keyboard, you'll have to fiddle around to make sure you know what key does what (as the way the android OS deals with key actions is different). On my TF201 tablet with keyboard, it acts exactly like a computer would. On my LG Spectrum phone (no physical keyboard) it gets a bit hairy because the screen is smaller, but for all of you fanatics who love ADOM (ME!!!), it's a small price to pay. I'm working on an android app that will auto save your save game files and back them up. I'll post as progress is made.