Would a vehicle speed sensor circuit cause a 1991 GMC truck to run poorly and if so why?

No. You have other problems involving the induction, fuel pressure, or spark on the engine. If the check engine light hasn't come on, then a good place to start is with is the fuel and air filters. If they are good, then next would be plugs and wires. Also look for vacuum leaks. We had an 87 that ran terribly, replaced all the above, and found out that the MAP sensor was bad. No codes coming from the PCM. Frustrating, and time consuming.