Welcome fellow Iowan!
As you suspect, the water in the reservoir will not readily mix with that in the radiator. However, as the coolant heats up and expands it will flow in to the reservoir, then as it cools coolant will be pulled from the reservoir. So after several long-ish drives you may end up getting all the water and lightly diluted anti-freeze mixed together. In the summer it's probably less of an issue if you aren't experiencing overheating, but as winter approaches you will want to have the freeze protection point of the coolant in the radiator tested.
-Rod