Depends on the program. Most don't since you're frequently on call, etc. My program you have to be PGY-3 or greater to be eligible to moonlight. So again, depends on the program. You'd be better to just make sure you maximize your experience in order to monetize it on the other end.
Not sure why everyone stresses "implants" as the best utility of a GPR/AEGD. Mine focuses mostly on oral medicine since that's the population I'll be treating for a few years. Restoring implants is easy money and doesn't increase your liability. I agree learning molar endo is a practice builder, as well as complex extractions and thirds.
A GPR/AEGD is a great idea for someone who doesn't have student debt (like me; scholarship). Especially if your GPR is at a program that allows you to make a lot of professional connections. Like the OP said, many offices want someone with a residency experience these days. Yeah, you can find an associateship without it, but is it ideal? If you have a lot of student debt and your GPR doesn't seem to do anything other than "get you up to speed," then yes, it's better to go directly into practice b/c the residency isn't going to advance your skill set and you're suffering financially because of it.
