I've never heard anyone say "I pass through the town on my way to work"; I've only heard "I go through the town on my way to work". Not to cause confusion (too late), I would say that in common speech pass means so many different things e.g., pass the chicken, the bill was passed, he ate beans and passed a lot of gas ;) The classic American usage is: "Howdy, partner. "Are you from around here?" "Nope. I'm just passing through". So to me, "passing through" means one could be hanging around a place for a few days. Like the river that passes under the bridge. Or the clouds that pass overhead. Clouds don't go overhead, they pass overhead, yet they may be floating over your house all day, before they "go away".
Good Luck!