Sure you can; HOWEVER, You'll find that some national carriers don't use uncovered pickups and others won't be happy with a part time arrangement. Since most of our work involves overnight drives, you'll get pretty stressed if you have a day job to get to. Most of our deliveries are scheduled for six or seven in the am.
For partime and weekend work you might be better served by checking your yellow pages for Couriers. It's expediting on a local level where you might have several local stops and be home every night.
Terry