It matters not what our input is. Traffic laws are state-by-state, and they vary. What you should do is get a handbook on the subject from your state’s DMV and see how the lows apply for you.
Check with your insurance company as well. Should something happen on that “brief ride on the street” you’ll need to know where you stand. If someone is injured and your insurance doesn’t cover it, you could be in deep do-do. Medical expenses can wipe you out, and if a civil suit gets filed the plot will thicken.
My personal opinion is that you should use the road shoulders if you need to follow a roads path, never the roadway itself. But your stste laws will rule.