Hmmm.... Hard to say without seeing it for myself, so I have to say maybe.
If the problem is a stain set into the paint, probably not. If, however, the problem is a residue build up caused by exhaust, then vapor cleaning could be very effective. For a problem like that, I'm guessing the machine would not remove it without the aid of an additional cleaning agent, but it might. If I were in your situation I would first try using the machine on a low pressure setting with cloth covered attachment/tool to gently rub away the problem. If that didn't work I would mix a mild solution of soda ash with very hot water and either pre-treat the attached cleaning cloth or the problem area, followed by the method I just described. I'm about 50% sure this would work, but since I haven't seen the problem myself, I am hesitant to say anything with certainty. I have, however, had very good luck with very tough grease/oil type problems using the vapor/soda ash combo. 100% environmentally safe & no fumes.
As you know, paint quality can vary greatly, so I would exercise caution and common sense along the way. Soda ash can be pretty powerful stuff when mixed at a high concentration, so obviously starting out by mixing up a mild solution first would be prudent. Same advice goes for the use of a vapor machine on painted surfaces. Use a low setting and pulse the steam button/trigger (don't just shoot it out full blast non stop.) Maintenance on an area like that once fixing the problem should be a snap using a vapor machine.
Vapor cleaning takes some practice to become effective and efficient with it, but can very effective.
On another note, have you ever tried a product called de*solv*it? It's pretty good stuff, if you haven't tried it. Much better than goo gone. There's a few different types, but I think the one I've linked here might help your problem.