Will a Chevy truck run with computer disconnected?

No, a modern Chevy truck (and most modern vehicles) will not run reliably, or at all, with the computer disconnected. The computer controls many essential functions, including fuel injection, ignition timing, and emissions controls. Disconnecting it will disrupt these systems, preventing the engine from starting or running properly. Older vehicles with carburetors might run, but even then, performance will likely be severely impacted and it could potentially be damaged without the proper computer functions.