Yeah, exactly. Kal wouldn't initially realize how morally problematic the Doctor can sometimes be, and it would only come to a head once those tendencies came to light. In the end though (after the pertinent conflict was resolved), they probably would still remain allies, not unlike Kal and Bruce-on-a-bad-day.
Since we're talking about the manipulative Doctor, I wonder whether Superman would be able to come to an understanding with Ace, whose shoot-first tendencies caused some pretty big clashes between her and the Doctor. Does anyone know how well Superman gets along with Jason Todd? That might indicate whether he could get along with Ace. Benny Summerfield, or course, would be absolutely delighted to meet Superman, and I think they'd get along really well. She's not far off from Lois now that I think about it.