Like brandon said it is a hit and miss depending on your betta, My betta ate a few when I 1st put them in his tank and now he could care less that they are there.
Mine could care less about the shrimp in his tank. He chases occasionally but I have a shrimp explosion going on, so I don't think he is catching them. I always see some of them out and about.
I agree, it's hit and miss. My betta would pick at the ghost shrimp that was in his tank, but after a couple weeks, he left it alone. It still died though. I'm 99% certain it was from stress.
i remember back when i have a ghost shrimp/betta tank the betta generally stay at the top of the tank, and because of betta's up turned mouth it is really hard for him to pick at the shrimp on the bottom. Not to mention betta is really slow.