Objects tracked on radar that cannot otherwise be identified would be intercepted as soon as possible. Investigation of UFO stories from the general public is what they don't do any more. Can't say as I blame 'em; I'm sure it's tiresome, going over the same old stories time & again.
The hypothetical Chinese pilot in a Russian MiG is a totally different thing. You may not know this, but our radar's usually coupled with a thing called IFF (Identification Friend or Foe). The aircraft info would be displayed on the screen, rather than a blip. If the pilot didn't respond to radio requests, interceptors would be sent to meet him. Given our current political situation, whether the MiG pilot responded via radio, or was intercepted, he'd probably be invited to dinner & a show.
During the Cold War, it was common to find US & Soviet air crews greeting each other when we did intercepts.