That's actually a very common thing for corporations to cheat on. So far, every corporation I've worked for has screwed the temp agencies out of their ridiculous fees and worked with the individual directly.
In temp-to-hire scenarios, often a significant percentage of the first year's salary is required as a finders fee, but I've never seen a company actually pay it if they thought they could get away with not telling the agency.
But here's what I really came to tell you: the ad agency knows the risks they run, and they are unlikely to just hand you the extra cash. It represents legal risk to them as well and with no savings they have no reason to go along. Additionally, they may actually find the agency useful (even though most companies see them as a last resort and would prefer not to use them it can happen) and think at least some of the fee they pay is justified.
I honestly don't think you can expect to pocket the difference as a raise that easily. I think if the ad agency wants to do it, they'll want to do it for their own savings and not for your raise. They might view the 40% as obscene much in the same way you do.