Shhh!! Don't tell my PC!
I don't want to start turning it off and removing all plugs now, as for years it didn't know that welding (TIG) was of any danger to it.
Seriously it may damage it, but as long as you don't weld anything that is connected to it, a modern PC can take a lot. One of the worst things you can do to it is to put a GSM or other handy-phone on top of it. My monitor really don't like that. I can see the screen twitch just before the phone rings! So far my files have not been electrocuted though.
But there is no reason to place the PC closer to the welding than necessary. One reason is that welding creates ozone, and ozone attacks rubber and some plastics. (Did you notice the insulation of the cable to your welder starts falling apart sooner than with other tools?)