Yup, it's certainly possible. Heck it's even possible to go from Amflight, your local Salt Lake part 135 company, to someplace like Southwest. It's been done before, but understand the first people out of the gates and into mainline hiring classes are going to be guys that are check airmen at regionals/nationals with good connections, a college degree and gobs of TPIC time in something possibly larger than an RJ. I.E. Moving from Air Tran or Allegiant to a mainline carrier.
As with most things in life, getting that job at the mainline carriers is going to be more of who you know once you meet the minimum qualifications.