Apps to check out:
I've tried them. I like them all; they all have different features. Papyrus and Lecture Notes seem to me to be the ones most actively being developed.
I would say yes, you could replace paper as long as you're ready with you TPT up & running with the app up when you need to start writing. I find I still use my phone (a Tmo Vibrant, no less) for post-it-type writing just because it's faster.