It's not critical to have a working lambda sensor, but obviously you get no closed-loop operation when you're cruising so the fuel economy (sic) will drop. - It doesn't really affect the performance seeing as you're on open-loop when you're on the power.
Yes, it needs to heat-up to operate. The GTiR runs a titania sensor (rather than the more common zirconia); so it's not about the voltage; it's about the electrical resistance of the probe. - That's why it's a three wire probe rather than two; one wire for the ECU to supply 1.0V, and the other two measure the resistance across the probe.
So low resistance when it's rich and high resistance when it's lean.