I don’t know. Why not?
I don’t think anyone in Denmark has done so – targetting the search engines, that is. But many other forms of outreach and promotion have been made. For example, for several years, my agency ran a netcafÃ© at the Roskilde Festival. But I guess it is mainly some of the private-public partnership initiatives, or outsourced solutions such as our digital signature, that have used ads.
Sidenote to directgov: It’s a pity that we users of Firefox are still left with a partly dysfuntional website, which however almost validates, so it might well be a firefox thing, so whom to bash on is questionable, of course.