Is there some place where I can check the IP addresses of the spiders Adwords uses to crawl websites?
Yea, you can get it by fetching the user agent string for the bots and recording their ip to a db. To my knowledge there is no "Adwords bots", just Adsense bots. There ip's change a lot, but their easily identifyable by their user agent. There might be lists out there, but you can easily get the info yourself.
check your log files. i doubt there is an adwords spider but you will be able to identify google bot visits.