Answer A: It'd be on the background check that virtually every company does now, so by proxy, yes I would. I'm not saying that every person who doesn't have a diploma or GED isn't qualified (or that the ones who do ARE qualified either!)...it's very possible they are. But there has to be a minimum level of qualification, and diploma/equivalency is a reasonably reliable indication of ability and commitment. If they don't have one, then the odds are that they probably DON'T have the ability or commitment to be a good employee. You have to separate the wheat from the chaff at some point...
Answer B: If I was hiring somebody to work for me directly, without the ability to get a background check...good question, to be honest. It's up to them to convince me they are qualified to do the work, and so it'd be STUPID to not verify every part of their application that I could, but where I would draw the "could" line at...if it was the only qualification they presented, then yes I would make an effort at verifying it, and if I couldn't...I'd round-file their app. They haven't convinced me.
If they had 30 years of experience, it's unlikely I'd see the need to go that far...unless they were giving me the heenkies already, in which case they'd be out of the running anyway.