GODS YES.
It's a case of "Yes, the links to site (x) are down, don't spam with with alerts that everything at that site is down", but unless it's programmed in like that (and by default, it is NOT!), it can quickly lead to alert fatigue.
The former boss I named El Turkey wanted us to get an alert on Every. Single. Switch. Port. in the event someone rebooted their machine, or something went down. our admin for solar winds said No, but if he insisted, that he'd be the one to get all the alerts.
You ever hear a phone just sit and do nothing but spam out 'text message received' alerts for ten minutes solid? It's not fun, and I've sat through that hell exactly once when we had a site go down hard because of the sheet number of crap that we have monitored there legitimately. But if there was an alert for each of the several hundred (or thousand plus, I think) switch ports? the phones would still be beeping away at us even though the incident happened several years ago...