I've been looking into something like this, as there are sometimes jobs at my home airport listed as part-time. I am self-employed, and my hours are whatever I want them to be, so I could handle working the 'bad' hours. I don't mind nights anyway.
I think the sweet spot is to find an airline that gives benefits to part-timers, but who also screws their frequent-flyers by restricting international upgrades to higher fare classes. Only chance you will have to fly in J as an employee. DL and CO would qualify, although DL's Ready Reserve part-time program seems to have restrictions on the non rev travel. I think it's 30 days annually, with only a portion of those allowed to be ocean crossings. No interline either.
The listings I've seen only pay $10/hour, but I could easily make another $50/hour in travel benefits.
Just about anything you want to know about non-rev travel policies is posted on airliners.net. Not so much about what it's like to actually work part-time at an airline. Anyone?