No. If hungry they may nip at them, but it is definitely possible to keep them together. Some would argue that for the shrimp to truly thrive they should be in a tank without fish, but it depends on how exactly you feel about that. I have shrimp in with cories, discus, platies, gold nugget pleco, angelicus botia, Synodontis petricola, serpae tetras, glass tetras, kuhili loaches, cherry barbs, and guppies.
It would be safer to start with cheap shrimp like ghost shrimp and if they do well then invest a little more money into the 'fancier' species like amano or cherry.