It sounds like Google might have a problem with the ‘sticky’ part.
This is from “Examples of unacceptable implementations” on the AdSense site.
###Unnatural attention to ads
Publishers are not permitted to bring unnecessary or unnatural attention to their Google ads. Examples of this include:
flashy animations that draw a user’s eyes to the ads
arrows or other symbols pointing to the ads
Drawing unnatural attention to ads includes placing Google ads in a floating box script that causes the ad to appear in a “sticky" position on the page as the user scrolls down. This type of ad implementation is not permitted.
Other than that it sounds doable.