If I have several threads running in my application, all of which have a while(true) loop with no Thread.sleep() in any of them to act as a ghetto action listener, would this negatively affect my battery life? By regular logic it should, however, I'm not sure whether the processor's constant monitoring of the while loops, would contribute a significant battery loss or not?
It boils down to what you do within the listeners/ while loop. If it involves stuff like wifi enabling sensors or CPU intensive tasks or network i/o then its pretty obvious ,else you should do just fine. Predominantly a few of the OS functions also do the same in the background.
However there seem to be better ways to handle stuff like this in android why not give those a try.