There is a rule against PA announcers talking while the play is being run, but it's a VHSL rule and not a NFHS rule, so it's not in the Rules Book and most officials don't know about it. I hate it when those guys do that so I looked it up in the VHSL handbook and, sure enough, it's there.
There is not a specific penalty but I put the kibosh on it whenever it happens. The reasoning? Well, it's annoying as heck, but the real reason is I don't want to have to listen to what they say to make sure they aren't giving an advantage to the home team. About 20 years ago, there was a school in the association I was in at the time that allowed their PA guy to do this and on one play, the opposing QB runs a great play fake. Over the PA you hear "IT'S A PASS!!!!" Flags flew all over the field.
I also had a play one night where some yokel was on there with limited play by play, but not too bad until the end of the half. His team was inside the 20 and ran a sweep to the far sideline, so this play happened every bit of 75 yards away from him. The tackler reaches high and gets a hand inside the shoulder pad but below the facemask and pulls the runner down. Over the PA I hear, "[kid's name] around the end, he crosses the 15. There's a facemask. THERE'S NO FLAG. THEY'RE NOT CALLING THAT FACEMASK. ARE YOU KIDDING THEY'RE NOT CALLING THAT FACEMASK." I didn't penalize the team but I did shut off the PA.
As for a rule about the PA guy keeping the clock, there is no rule but common sense has to prevail, you would think.