Yes.
If 'professional pilot' to you means 'airline pilot' including the stupid hat and easy to wrinkle shirt, then no, without a degree in something you are probably not going to get in.
If 'professional pilot' to you means: Make at least part of a living flying a plane around in some capacity': sure.
Tomorrow morning 'Bob' is going to fly a 152 from here to Colorado and bring back an Aeronca Chief on the way back. He is as professional a pilot as you could find anywhere and he makes a couple of bucks doing those flights, but you'll never see him in anything but jeans and a scuffed leather jacket.
If you can afford to make it work with your schedule, you can do the requisite certs like commercial and CFI piecemeal, either with your local school or by going to one of the training mills. With a flexible schedule from your bread job, you can instruct or contract fly quite a bit on the side.
Once you notice that aviation is not only shiny jets but also flying an attorney in his 210 to a deposition or a construction manager to a jobsite in his companies Cherokee Six, the task of becoming a 'professional pilot' doesn't become insurmountable.
Fwiw, based on the age structure in the pilot population, there WILL be an opening up of positions at all levels over the course of the next 5 years. For every 65 year old who finally gets pried out of his airline cockpit kicking and screaming, there is a job at the bottom rung (CFI, drop-zone pilot) opening up somewhere.
