Can a batter get a base hit and have a fielders choice on the same play?

This would be a hit. The only scenerio that this would be a fielder's choice is if the bases were loaded during the hit and the runner that was thrown out was on third base during the hit.

A fielder's choice is scored only if the batter would have been out had the fielder chosen to go after him instead of a runner already on base. If the batter would have reached first anyway (such as in the scenario described here), he would get a hit.