Mmm... Dunno...
I don't speak from personal experience (I'm sure someone who has will come along soon), but I was thinking of getting a betta and I have done quite a bit of reading.
From what I understand it's very much down to the individual betta. Generally they will eat the shrimp, but occasionally you get a fish that won't. If you get large amano shrimps, that are larger and more aggressive than other species, they have a better chance of survival.
... and now to the betta experts to confirm my research or inform me I've been reading in the wrong place.