I think the engine still can be cranked if transponder portion of the key is inside, just like a tradition vehicle without an immobilizer since it's defeated by having the transponder key in the car, unless there's also an aftermarket alarm with starter-kill. With knowledge on how to hot-wire a car, that TL-S still can be driven away.
I haven't kept up or looked at aftermarket alarm solutions. But I believe the only way it would be safe is if the transponder code is programmed/recorded into the actual remote start unit. And only if the a remote start command is received, the transponder code is sent to the vehicle's ignition system to bypass the immobilizer.
Experiment:
I've yet to try this, but if you have a non-immobilizer key like a cheapie spare key for the door locks only, put that into the ignition and hold your transponder key next to it. If you can fire up the engine, then even cutting off the teeth portion of the key won't stop the vehicle from being stolen traditionally by breaking the ignition lock. It just makes a little more difficult for the thief to find the key and putting it into the ignition and drive away.