Can I grow a cane-stem begonia in a betta tank?

on a regular basis, I water propagate my cane-stem begonias (I believe they are either an Angel Wing B. or a B. Marguerite DeCola). I've been wanting to put those that I am propagating in my Betta's tank but I am worried it could be harmful. I've seen things on the web which say that cane-stem begonias are not poisonous to humans or pets (dogs/cats) and that it is generally fine to grow a variety of plants in a Betta tank. I was hoping someone here had firsthand experience in these two organism's cohabitation. Besides toxicity, I'm also concerned that the tank does not have filtration. I'm guessing if the begonia is not toxic to the betta, I'll at least have to change the water more often and cut back the begonia roots to avoid rot.