^
Spoiler Below I don't think so, actually. The usual monty hall conditions aren't in effect because he wasn't equally likely to pick either of the other doors. In the monty crawl variant, the information you know about the methodology by which he picks the door makes it equally likely that the car can be won by switching or not switching if he picks the lower numbered door.
I'm not sure how your explaination adds up to 2/3. There's only a 1 in 3 chance he'll pick the higher numbered door, and a 2/3 chance he'll pick the lower numbered door. If your odds were 2/3 for switching when he picked the lower numbered door, you'd win by switching 1/3*1+2/3*2/3=7/9 times.