Not that people are clamoring to say hi to me while I'm on the road, but I do get a number of requests to catch up before a show or on a day off. It's a balance of Al fans, forum & facebook friends, garnered over more than 22 years of being online (not that there's anything wrong with that!) and personal friends and relatives.
As several members here will attest, I am typically available and look forward to putting faces with (user)names. But there are reasons that I may not be able to connect, including prior commitments with friends/family/industry, travel/time constraints, or venue constraints, and I know that other touring musicians have the same kind of conflicts. On the other hand, local gigs are usually a different thing altogether, and much easier to shake a hand and take a pic.
But no player should be so busy that they cannot respond, even if it's a stock reply saying that they get a lot of emails/msgs and can't always digest each in a timely manner. If they are simply too busy to deal with casual contact, there's auto-reply and ways to avoid receiving messages. If a message was read, it deserves a reply.
Bermuda