Will a pilot stay lit with a bad thermo couple?

No inless the gas valve is bad.

Will a pilot stay lit with a bad thermo couple?

If the gas valve is bad it could keep sending gas to the piolit. The odds of this are not very good.

How does the thermo couple control the pilot?

How does the thermo couple control the pilot?

When it gets hot a signal is sent to the gas valve to keep the flame on. If it is not hot enough or the t-couple is bad it will go out as soon as you let go of the botton on the gas valve.

No a pilot will not stay lit with a bad thermo couple, unless , as Josh stated, you have a faulty gas vavle. One way to test the valve is to unhook the thermocouple at the valve and see if pilot goes out. If it does go out, then the gas valve is good and the thermo couple is doing its job.

There is one other possability here. If your furnace is very, very old, the thermocouple may not be controlling your pilot, it may be controlling a box that will only shut off the main burners. Please let us know why you are asking this, and if you could post some pictures of your gas valve and pilot setup, it would help.

Good call on the baso valve. I never thought to think that far back. Lol More info as to why you are asking will defentally help.