Overall, i wouldn't worry to much about the stigma that G7 pilots won't have a career at the majors.
Currently, I have numerous friends at G7, mostly out of circumstance, they were furloughed from 2 or 3 different regionals and the only company that was still hiring was G7, end result was that's where they ended up. Take note, none of those friends started with G7 as their first choice regional, or even their second choice, but when things got really rough, they were willing to take the plunge.
I'm no longer in the biz, but still in an aviation related field that employees plenty of former pilots, and I've hired several G7 pilots in the last 12 months. There have been instances where G7 pilots faced some scrutiny, there was a JetBlue pilot who (at a hiring event) screamed, yelled, and cursed out a G7 pilot who was looking for a job...that particular JetBlue pilot was released from service pretty quick. Don't know if the G7 guy was hired, but i'm almost certain that most G7 pilots have the ability to get on with the majors, as most majors don't know, and don't care about the drama going on in the kindergarten classroom known as the regional airline biz.