Absolutely. Linux is the unsung hero of keeping hardware relevant. I have a personal server that’s been running so long that I’m afraid to turn it off in case the drives don’t spin back up again. (In fact, it was the second server I ever used to run Boing Boing on!).
But lets not pretend that we are in any way the majority of users. 
What’s amazing to me is that these systems (the server I mentioned) have been exclipsed in almost every way by what’s in my pocket now. certainly in IO, RAM and graphics handling, and more than likely in CPU capability as well. I’ve recently begun to realize that my old gear has less and less utility because of 1) superfast internet and cheap online storage for things like media where privacy isn’t an issue, 2) the fact that modern media needs fast subsystems for things like lossless audio, 4k video, and so on, and 3) how horribly unprepared anything before USB3/thunderbolt is to handle that sort of traffic.
On-topic:
I’m not personally concerned about old PCs on the network. Anything in the last decade can be configured to have a firewall, and since they’re general-purpose computers, they can be configured with a modern browser or, at the very least, in a setup where you carefully control what destinations you visit. It’s these devices that were designed to be directly-connected to the internet with open ports that are the problem, and I think we’re going to keep having issues as long as they’re designed that way. Have these things poll a control site for remote content and interact that way, don’t put services directly on the 'net unless you can control them!
