You’d need to define what you mean by old generation. But to answer your question in a generic way, in order to support gigabit internet, the whole thing needs to support gigabit speeds. If any part of the system doesn’t support gigabit speeds then that will be the bottleneck.
To me, old generation PC would be one that would use a serial port to communicate with the modem, in that case, I don’t believe a serial port could process gigabit input.