On the one hand, definitely not. For Usenet in 1981, there weren't anything like "dedicated powerful news servers".
Usenet itself is older than Internet and possibly older than ARPAnet; initially the news spools were kept on the same computer (e.g. a university's Unix system) that everyone logged in to from their local terminals – the same system that employees or students used for mail, text editing, typesetting, and other stuff; so definitely not a "dedicated server". Programs like rn used to simply access /var/spool/news, and to this day you can have email delivered to /var/spool/mail/$USER.
Also, for a long time dial-up UUCP links were their primary mail & news exchange mechanism, creating a peer-to-peer mesh – the closest thing to "dedicated server" would have been a few popular hosts with a lot of peers, e.g. decvax. "Bang paths" (host!host!…!user) come from UUCP. You can find an old news archive at OldUsenet.
But on the other hand, maybe even earlier than that.
The computers (minicomputers and mainframes) used by companies and universities were already significantly more powerful than the average personal computer of that time, with much more memory and disk space, and possibly hosting several dozen user logins at once – acting as a "terminal server". So maybe you could say that servers were born before networked hosts. (Disclaimer: I haven't checked actual dates of when things happened.)
So I would say that there really isn't a single point in time when someone "invented the server" – I do not know the history well, but it does seem that this sort of thing just gradually evolved.
After all, the first "web server" was merely a NeXT workstation with "do not turn off" written on it. And many people used to run dial-up BBSes off their own PCs, with some more disk space added – those were dedicated, but far from "high and powerful".