I have a ghost shrimp in both my betta tanks. Gandalf likes to "play" with his shrimp, who's name is Dyson. Sometimes, but not always, Gandalf will sort of follow Dyson around, almost like he's trying to sniff him, like a dog would to something he's investigating, but if Dyson stops running away, Gandalf stops chasing him. Gandalf is an extreamly passive, calm, yet curious betta, nothing upsets him!
Now Merlin is another story, he trys to chase his ghost shrimp, who's name is Hoover, but Hoover is a tough little guy and won't "play", he just ignores Merlin or will even chase Merlin sometimes but mostly they ignore each other. Merlin is much more attached to his Zebra snail, Nessy, follows her everywhere, lol.
Neither of my bettas have actually tried to eat the shrimp thank goodness. :)
On another note, Dyson and Hoover have both shed their shells a couple times and have grown quite a bit. I've had them for about 8 months now.