(Edit: in fairness, that would be more like "land line texting" than email.)
That said, it seems most of them were operated over dedicated networks. And the one i can find a reference to that was operated by AT&T had their own area codes etc.
All in all i get the impression that it could be done, but likely only so at great expense. Consider that having a ticker tape printer in your home suggested you were someone with great wealth that was watching the stock market 24/7.
Even having a telephone was not chump change. My parents talk about having one phone for several households, with the bell patterns used to indicate who it was for.
I suspect we should not underestimate how much the IC and packet switching has driven down cost of installation and operation.