It could be about a 3 mph increase if you have big knobbys now. If you have semi slicks now that are smooth not as much maybe 2 mph or less. It depends on a lot of things but that's the ballpark. If you have huge knobbys now and you get thin high pressure tires for the MTB you may get 1 mph improvement. You could experiment with your position as well.

My best mtb to a touring bike I pick up 2 mph and another 1 mph to the lightweight racing bike.