I went from 121 regional (just under 2 years) living outside DC to 91 Captain/Chief Pilot in a city I actually wanted to live in (6.5 years) to 121 major airline FO.

Worked out GREAT for me, caveat emptor and all that. I was admittedly fortunate to work for a small company with an excellent boss who was fiscally conservative, liked airplanes, and needed them in order to run his business...allowing me to stay employed during the Great Recession.

Yes, should you meet all the basic qualifications, you should be able to get a look at a 121 LCC or major down the road as a 91/135 pilot. As mentioned, however, time builds slowly in the bizav world so your end goal is something to consider.