Also, when you say you "don't have to use many busy roads" does that mean you do have to use at least one? If so, how busy are we talking about here? If you've got to go 1/2 a mile on a 65 mph divided highway to get to work, you might not enjoy that much. If your route to work is back roads and maybe you cross a 65 mph divided highway but not actually use it, then that's not so bad.
I wouldn't recommend buying a Grom on a saturday and starting to commute on it the next monday or anything, but 2 minutes from the house should be pretty doable. Also, the Grom is really easy to ride. My first bike was a 600cc Triumph sport bike. I took my MSF course and then practiced for another week or 2 in my neighborhood before even thinking about riding it to work. I'm pretty certain that had I had something like a Grom, I could have built skill a lot faster.
I'd pull the trigger.