If you were to put a high end MTB shock fork on that frame, it would raise it several inches. But a cheap zoom fork, that's only going to raise you up an inch at best, after you get on it and it squishes down. A cheap fork will be all you can find if its really 1". Bet though, its 1 1/8, because a townie is not a walbike, bike shaped object.
But yes indeed, an inch higher in front does change the angle of your steering, and definitely affects the ride. Raking the fork out longer will make it ride more cruiser like. But its already got that, so more could be too much. So don't put an 800 buck fork from a downhill bike on it, with 300 mm of travel. A zoom fork will have at most 100mm, and then will drop to 50mm when you get on it. 50mm you can handle without much change in the ride.
My wifes townie did have a shock fork, but it no doubt also had a different angle on the head tube.