If it runs Windows it'll run Linux almost certainly. The cheaper you go, the more likely you'll have lower priced or older components for WiFi, Bluetooth etc which may mean that you have to dig some firmware binaries out to get the whole thing running.

If you can take a USB stick with you of a typical Rescue distribution, and can boot it up, you'll know what will and won't work easily. The bits that don't work may need some minor fiddling. As I said, there are usually walkthrough blogs etc around.

Have fun.