Hey Amber,
I think it's a cool idea in theory but usually naturalistic tanks with mixed species are VERY big. If you have a big enough tank anything is possible. Keep in mind that turtles produce a ton of waste and require frequent water changes. The water changes might be too frequent for the fish (not sure on that as I'm mostly a reptile keeper). Also, make sure it's legal to keep native fish as pets in your state. I know where I live there are some native species of fish and turtles that we can not keep in captivity or that require permits. The turtle may nip at the fins of the fish but in my experience if the fish is too big or too fast it will simply become a tankmate. If you have any more turtle questions let me know!
Best wishes,
Mike
leafturtles.com
thegeckopad.com