Looks like you have it wired up and good. The signal wire (odd color) is the only important one to have correct. With the other 2 wires that should be the same color, one goes to 12v, the other to ground.
Regarding your question: If you are only remote starting your motor to warm up, then you are OK with this. The O2 sensor may not function at this time w/o the 12v source, but your motor should just run in open loop until you actually turn your key.
I wired mine through a relay triggered by my fuel pump source. This way it is not constantly on if I have my key on / motor off.
Based my wiring off the picture of that grand national plug.
Didn't think of key on - motor off.....but i really don't see that condition ever. I've got a separate switch to run my radio on w/o key, so can't think of a situation that i'd have the key on.
So, does the 3 wire o2 work without power? Will it work, unheated, like my old one......or not at all?

