+1 for Adastra and Carpenter!
You can do it, but like adastra said, catching them is a pain in the a$$. I have 3, and so far I haven't had to do a complete 100% change (my tank is cycled) hopefully I never will have to, because those little buggers are so difficult to catch.
Sometimes shrimps eat bettas poo (mine only do occasionall), but you'll want to sink some sort of food for the shrimp every 2-3 days (I prefer doing so daily) to make sure he/she has enough food and won't be hungry enough to attack your betta (it has happened to people before).
They live a while, however the first two weeks, expect them to drop like flies. I first bought 6 shrimps to go in my 10 gallon, and less than a month later, all but one had died (he's still with me)
- to avoid so many deaths right away, ask how long they've had their shrimps, and try to get ones that are active. If they are easy to catch and look sick when you see them in the baggie or breeder cup, ask for different ones.