From my experience they really don't care if you watch. That said, I usually don't hang around while they're laying, since:
1) It can take hours! And yes I've sat around and watched a hen lay, mostly because I was dying to try a truly fresh egg (doesn't taste "better" IMO).
2) If they do see me, sometimes they'll pop out of the nest thinking I have treats. Though sometimes they'll squeeze the egg out real fast and then run off to look for a treat. Either way I hate feeling guilted into giving out a treat.
But yes the egg song can be a very random thing. Sometimes I hear all of them singing, sometimes no one sings, sometimes they sing but there's no egg. The song can go on for a few seconds or for 10, 15 minutes. I have noticed mine are more likely to sing in the morning vs. afternoon.