Sure you'll go faster, but it most likely won't save you much time.

From slowest to hardest ride, I'll save only about 5 minutes on the 7 miles road/MUP portion if I never stop for a light and never have to slow for anything.

I specify road/MUP for that because another good portion at each end is parking lot, and how I ride there (ie, 6-10 mph) can take several minutes extra. So if I really wanted to save time I'd concentrate on going faster safely in a parking lot instead of faster on the road.