Tetras tend to nip the bettas fins I am sorry to say. Since the bettas do not see them as threats they tend to just allow them to do it and then the bettas end up with infected fins. I have not heard that the Cardinal tetras do this but the others all seem to do it. I do not know that I would try it but I cannot tell you not to do it. It is definitely up to you and I do know it would make a really nice looking tank but it would be my recommendation that you definitely have a back up tank in case the problem comes up so you can move the betta or the others if you have that problem. The betta will not probably bother the tetras though as they do not usually see them as challenges.

Rose