I agree. Adwords is not going to get you indexed. It will get you noticed, and that may get you links and from that getting indexed may happen. But the getting links is the main part here. Adsense ads (powered by adwords) are dynamic links, not 'live' ones. That is: they don't get indexed as links.
Good question. I wonder if you added adsense code on a brand new site, will Google discover that new site and index it even though you have not directly submitted it?