For the US history SAT II, would taking the AP history exam count as adequate...

If you mean AP US History, I think it definitely would. I took AP US History my junior year, took the exam in May, then the SAT II in US History in June and ended up doing pretty well in it, so in my experience, what you said works.
 
I myself assumed studying for the AP alone would be enough for the SAT II, but I ended up doing great on the AP and really average on the SAT II. I got the impression that the SAT II for US history is much more detailed than the AP for it. I'm thinking if you study from an SAT II book, you should do well on both.
 
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