I'm thinking about putting an over 18 verification on the pages on one of my sites with adult content, but worried that google wouldn't be able to index them then. Would it break any rules if I had it ignore the age verification just for googlebot?
I wouldn't think so, allowing the bot to see 'protected' pages is exactly what the NYTimes does. Also, it's not against TOS to block it either.
Adsense and the bot are two totally different things. You are fine with a warning page, google will index it as any other page/site. Stay away from trying to hide the warning page from the googlebot, it could get your site banned for cloaking without any benefits on the other hand.
You can use "noindex, follow" on the <head></head> of verification page so bot can start indexing with the next pages