Google Adwords will show you what keywords the visitor/clicker searched for, when the ad they clicked on showed. The point here is that you will of course pay Google per click made on your ads.
If you are ok with that, then yes, you will se a history of which ads were triggered/showed by which keywords "that the visitor typed in". Yes, if you go this route you will indeed see alot of keywords that were actually typed in.
Ian