I know a lot of people get their backs up if you call Panda or Penguin a penalty but to me it's all the same. If or some reason Google is causing you to rank significantly lower then in my mind it's a penalty. But really it's all semantics. If the site is truly ranking lower because of branded links then there's either a manual penalty or penguin at play.

I've seen this happen where a site buys an EMD and then names their company after it and then subsequently gets links that are branded but in reality they are only branded because they were lucky enough to buy an EMD.  Does that make sense?  For example, if someone wanted to start a house painting company in Anycity and they see that anycityhousepainters.com is available then they name their company "Anycity House Painters".  The branded links that come to them are indeed branded...but they're also an attempt to manipulate the serps.

I think that if you have a brand name that is the same as a keyword Google may not look at it as a brand name.

As far as "balancing this out" goes, it depends on whether or not you've really been penalized.  If there is an unnatural links penalty then that needs to be dealt with.  If there's a drop on a Penguin refresh day, that's a whole 'nother issue.

It's also possible that the drop has nothing to do with the branded links.

But, I think that Scott gave you some good advice on ways to link to your brand.

Adwords really don't have any effect on your site's rankings at all.  The links that come from the ads are nofollowed.