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.
You can but visitors will receive a message that your site contains secure and none secure data in internet explorer. Most other browsers have a way to communicate this state aswell.