First of all, welcome to WebmasterWorld.

I'm not sure I can give you an absolute answer to this one, because it depends on how the website that shows the banner constructs the link.

Many sites use redirects for banner ads to keep a count of the number of times the banner was clicked. In this case the link may show up something like click.php?dest=yoursite.com. In this case, it may not count as a link.

Also, Google is encouraging website owners to mark paid links with the nofollow attribute to distinguish them from natural 'editorial' links. If this is the case, then the link definitely won't count.

I think that graphic links in general carry less weight as links than text links do, because they don't indicate to the spider what the topic of the link is. Therefore, your banner link may count, although not for much.

Finally, Google in particular is trying to differentiate between paid links and natural links. While no one is sure how much progress they have made in this area, they might look at a graphic link that has the same dimensions as a typical banner ad, and discount its value.