Based on the manual I'm looking at, the two additional wires in the TPS harness connector are for the injector, so, no, the engine won't run with that disconnected.
I have no "hands on" experience with the 8v TBI systems, we didn't get them, our 8v models came with a carburettor, but the basic principles of fuel injection system will still hold.
View attachment 110613
This diagram is taken from a Suzuki FSM, I don't guarantee it'll match your Tracker, but it should be similar, I don't know if you have the tools to back probe connectors, and I don't know if the Suzuki connectors allow the use of back probes, not all manufacturers use connectors that do - #5 is your throttle position sensor.
"Back probing" is the technique of inserting a test meter probe, usually a very thin probe, into the back or "wire side" of a connector so that you can make measurements whilst the connector is connected to the device. In the absence of back probes some people use needles or tee pins to puncture the insulation on the wires, if you do this you need to make sure the needles/pins cannot short to one another or to any adjacent metal, and you need to seal the punctures afterwards
using something like liquid electrical tape. If moisture gets into those punctures it will corrode the copper inside the insulation, and cause problems down the road that will be very
difficult to locate.
Meter on 20 VDC scale (assuming a digital meter, but any meter that can measure 12VDC can be used - my preference for this is an old style analog meter, I'll explain why in a minute)
Black meter probe to GND, which is a grey wire with yellow stripe.
Red meter probe first to TPS In, which is a grey wire with red stripe, you should be seeing 5V or close to that.
Red meter probe next to TPS Out, which is a grey wire with no stripe, the voltage here should be between 0V and 5V and should vary smoothly as the throttle is opened & closed, with digital meters, the readings tend to jump around, with analog meters the smooth swing of the needle is easier to see, if you can see the needle flickering, jumping either to 5V or to 0v, it means the wiper in the TPS is loosing contact with the traces inside, and the TPS is defective.