Question: I know there is no such thing as a dumb question but this is: Can you serve contextual based ads via adsense or others on a site that is entirely behind https?

Answer: 
[AdSense now supports HTTPS](http://googledevelopers.blogspot.com.au/2013/09/https-compatible-ad-code-for-adsense.html). Just remove the "http:" portion of the ad code.
Yes, as long as the website is not protected by SSL certificates (in that the client accessing the website needs to have a certificate) Google is perfectly capable of indexing your site for keywords to cater the right ads for your website.

I am not sure if Google makes the adsense code available over SSL as well, if not your visitors will be warned by the browser that the page may contain insecure elements. I do know that their analytics code (For Google analytics) does contain an SSL possibility.

In case you have any more questions, Google's adsense support team/faq will be able to better provide answers to your questions, since you can let them know what site you are talking about!