The problem with betta fish is that they actually tend (I repeat, TEND) to preffer smaller tanks and can actually be stress by living in a huge (relatively) body of water. They are also going to be more aggressive to other fish that have large fins and will nip/fight with them. Your platties may fall into this catagory.
I really do not think that your neon tetras would be a super huge problem for a betta, but I also agree that a definate answer to if a betta would be ok in your tank would be hard to come by. I have heard some pretty big horror stories about keeping male betta fish with females as well, so it is absolutely true that it could, or could not work out. If you are intent on having a betta fish, maybe you could try it out and if it didnt work, find a nice 3 to 5 gallon tank for him to live alone in. It would be the best comprimise I could think of.