I've got a Worksman Industrial Bike. Gearing is 44/22 with 26" wheels, and fairly heavy.
On flat land, 15mph is about the maximum sustainable speed for me. Over longer distances, somewhat less. Last time I did the White Rock Lake/Creek trail, I averaged 15.0 mph over 22 miles or so, and felt like I was really flying. You sort of get used to the "spinning out", but it does slow your average speed.
This bike works reasonably well on hills. It will make a major difference how long the hill is, how steep it is, how many there are. What I found in riding on a few hills was that you're in good shape on the first one, but once your legs start getting tired, you can't downshift, and then it's either stop and rest (what I do) or walk it up.
The amount of fatigue in your legs does not always match the height of a hill. Trying to do a hill in too high of a gear will just kill your legs, more so than spinning up in a lower gear.
If the hills there are long enough and steep enough, beware of using a coaster brake as well- it's not just the uphill that's the problem.
Anyway, on your overall plan, if you already have the bike, just go ride it and see what you think. You should find hills you can't climb and some you can.