No it wouldn't. Pagers as I used them received the same signals all through the country. The network didn't even know if the pager was on or not. It was purely one way. It supported numeric (and tone) and even text messages (not encrypted but this day and age that would be possible). You could be out of coverage but the pager would warn you and due to the low frequency and low bandwidth coverage indoors was excellent. The only time I received an out of range message was when I visited a cave system.

Transmitting pagers with sending and receipt confirmation did also exist at one time but that's not the ones I mean. Maybe a network will emerge again. It doesn't actually cost a lot.

I'm kinda hoping more people will want their pagers back for precisely this reason.