Battles over the use of trademarks in click ads have been fought in the courts for years now.
Is there any problem with you running click ads against search terms, or even using the name of a competitor in your ad?
There have been enough victories on this front that it is a pretty much settled question with Google. Yes, you can do that.
It is entirely another question whether this is a useful strategy. Our tests indicate that in most situations, it will generate very little traffic. People looking for a particular brand or company are looking for that brand or company. Even if they find themselves on your website, chances are they’ll just think they made a mistake (or you did) and hit their back button.
It may help build awareness of your name amongst prospects who have heard of a competitor only. That is more of a long-term strategy, but it doesn’t cost much to include it in your program. Just don’t count on it as a major player.