Well, I ran wget with the arguments I gave and I got a complete local copy of my own site. It changes all links so that they work with the saved files, whether there are question marks or not.
It's not really server side, since wget is a http client (like a browser) but I ran it on the same machine as the site was on. But as long as you have wget you can run it from any place you want to download the files, it'll just take a bit longer to transfer everything over internet.