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Public / private is only an issue for Windows itself: to determine how it should set up your firewall and what Windows services it can provide on the local network (Windows won't try to provide file shares on a public network, for obvious reasons...).
At best Windows will ask you about firewall exceptions; most games which use a network connection request such an exception to be added, for which you can simply use the default(s) provided by Windows itself.
But yes, even if you would deny access it could still work because those firewall rules (now talking about GTA V in specific) apply to incoming data and well.. unless you reconfigured your Internet router you wouldn't receive any new incoming data in the first place because the firewall on your Internet router would normally block all of that first. There is uPnP but even that has its limits, and is kinda irrelevant here.
Bottom line: accepting the defaults should be enough. Just treat GTA like any other game which requires a network connection.