Is it legal for me to just pop my affiliate URL into Adwords campaigns and try to get conversions that way?
you need to read the terms for the specific advertisers. I've done my research and A LOT of the advertisers don't allow it (at least the ones i've checked). Make sure you check before you do it. It would suck to do it, pay adwords only to have CJ commission be rejected because you didn't respect the rules...