Yeah, but you don't want just any old laptop to do that on. Like if you were to get one of your old laptops from 10 years ago that you were downloading a whole bunch of sketchy stuff on through limewire, I wouldn't think to recommend using something like that. The most secure way is to buy a cheap laptop that has no wireless or bluetooth capabilities, and then load trusted/gpg verified files on the computer through booting it on a live-USB.
Using an old processor doesn't also mean you have to use your old (non-wiped) hard drive.
An old laptop with a formatted hard drive and wireless adapter removed does its job very well.
There is also no need for running an OS as live version from an USB stick. It is absolutely fine to install an OS to your hard drive.
No connection adapters mean no connection. Regardless of the OS you are running and from how you boot it.