The previous owner of this house put drywall up but didn't finish the walls. It looks like the drywall has been there for years and it's quite dirty. My question is: Is there any reason I shouldn't be able to just clean the walls off then tape and mud them up?
You don't even need to clean anything unless the soiling is greasy or would otherwise inhibit bonding. In fact, you risk damaging the unprotected paper surface of the drywall.
I'd do your taping and use a good stain-blocking primer/sealer over it all.
Use a wrung mop, to remove any dust, and a drywall knife to scrape off any "boogers", before finishing. You would be surprised what can get stuck to a wall over time, and end up in your mud.