This might not be done since this means changing the underlying code of the forum system and not just templates. I am against changing code unless really necessary since it makes it really difficult to upgrade the forum to the latest version.

If the forum categories is properly constructed, you can easily just go to the parent category, and do a search there, encompassing all the child forum categories, without even going to the 'advanced search' page.

Here's an example. In this case, if you are in the Software parent category, the 'Search this Forum' option will automatically search all its children categories.