I did this for years and years as a part time student at a large university eventually earning a degree in the sciences - got stuck in the lost generation of the 2000s, had plenty of time to indulge. It was a pain and my GPA took a hit due to scheduling conflicts but it was worth every penny. I took as many T-Th classes as possible so I could just fly 4 days F-M. When classes were MWF or MTWTh I would try to bid 4 day trips that started late on Friday afternoons and then hope to be able to drop the Sunday night overnight allowing me to make the Monday am class after which I'd rally back to the airport to finish the last victory lap of the original pairing. Th-Sn pairings with a later show time also worked well and the benefit of bidding weekend trips is that you gain a little pseudo senority as most guys wanted weekends off.

Downsides: it didn't look good on my applications (to the majors) since it wasn't a clean and pretty 4 year degree done in 4 years or less. GPA took a hit due to difficulty of the degree and missed classes. As other guys posted, and especially because I chose a tough degree, I gave up most of my social life, spent every free minute getting in study time (flash cards on airport parking bus, reading during airport appreciation time), and was often running back and forth between the airport and university. It was a stressful time.

Upsides to how I did it: besides all the obvious benefits of quality education, having a non aviation degree offers alternate career options if needed. I also didn't feel that online degrees were worth the time and $$ nor did I find them to be given much respect from people in general.

So yeah, you can totally do your degree while working at a regional. Obviously the online route with a degree in aviation is the fastest and most convenient route but if you wanted to go to an actual campus and do something different - where there is a will there is a way.

Best of luck.