The SUB BAT relay's coil is connected to something with IG in its label, so it looks to me like your 40A battery lead is indeed controlled by the ignition switch.
However, you'll want to verify that with a VOM or test lamp before you rely on it. Also, in the case of something like a depleted AGM battery, you might want to carry a few extra 40A fuses. (On Edit: Actually, I'm not familiar with the symbol used by the 40A, and it's different from the fuse symbol, so it might be a circuit breaker, in which case no fuses are required).
You'll also want to be sure that whatever return path exists between the TC batt and the Tundra's charging system is heavy enough to handle the return (aka ground) load of both battery charging AND all the lights on at the same time. Gets even worse with trailers if they have brakes...