Would a temp gauge still display the right temp if the ECT wasn't working?

 

Yes

 

Ok, I'm trying to think wether or not my problem could be due to the ECT... also, will the ect sensor or the speed sensor display a CEL

 

There are CEL codes for both circuits, but a problem with those sensors doesn't always throw a code. In the latter case, certain electrical tests (described in the service manual) can be performed to test whether those sensors are bad.

 

ECT just lets the ECU know when the vehicle is warm, then sends it into closed loop

 

Well, I'm having idle problems,and my gas is going fast... and I'm having poor cold start up.... I'm thinking it could be a mix of clogged fuel injectors and the ECt...