Yes, safe to assume that many majors do, and some regionals as well. If for no other reason than some of the interviewer pilots and even HR staff are interested in their industry and come here to see whats up.
Hard for them to get your IP address without doing some (probably illegal) hacking though.
Personally I view APC as kind of a neighborhood bar, I don't exactly expect folks to maintain the same level of professionalism that they would at work (ie it's OK to vent within TOS limits). Much as I might want to, I would not hold someone's APC opinions against them in the real-world. Well maybe, but only in extreme cases where someone's mental stability was in doubt.
But I wouldn't bet on everyone else making that distinction. We've all seen what happens when exuberant off-duty behavior and even personal opinions that used to be perfectly common, but under the radar, makes into the public realm via facebook, etc.
If you're still upwardly mobile, probably best to either be on your good behavior...or be damn sure that there's nothing in your account or what you post that can lead back to you. Remember, there's no "burden of proof" or "reasonable doubt" here...if someone even suspects you might be "that guy" odds are they'll hold it against you.