The other way around actually - I believe that tetras tend to nip at the fins of bettas. It's a shame though. A tank full of neon tetras and a betta would be beautiful. But then again, so would a tank full of bettas
The neons would nip the betta to shreds most likely. And the betta might mistake the platies for female bettas or just be annoyed by their bright colours.
It sounds like a great community already, a betta might just cause trouble.
My neon tetras stay a few inches from the substrate and don't even come up for feeding. I have to have food drop through for them. Would they even notice the betta at the surface?
How about doing a separate thread on this- or trawling through old posts with the search function? My impression is that several members have kept this combination- some have done well, and others have had bad fin-nipping problems. It seems to be luck or unidentified factors in the setup or the individuality of the fish. The betta in the community tank seems a bit of an unpredictable adventure altogether.