No cts cannot cause engine to die all of a sudden, but Map certainly can.
They do not have a LOS/LIMP facility in the normal sense, as they are too old for this.
Instead they will if they lose a signal go and have a mental session, to check cts simply unplug, and it will lean right out, to check tps unplug, you will soon see a change in behaviour.
If you have not changed ti in a while I would change the cts anyway as it is so important that it reads correctly, usually when duff they overfuel due to it reading colder than it is, or just put a 0.27 K ohms resistor across the pins in the plug for cts to simulate a warm/hot engine at 90C.
Test the tps etc.
tabetha