Custom search taxonomy with depth

I am trying to configure custom search using taxonomy to do something that I consider should be a relatively basic requirement that most users would like to do. Imagine a I have a top level taxonomy vocabulary called catalog and within it I have something like this:

Clothing > Men > Shirts

I have restricted my custom search to only show the top level taxonomy to be selected. If a user selects Clothing and enters a search term, I'd like the search to match any node that has a term clothing or any of the child terms for clothing e.g. Men and Shirts.

Is it possible to achieve this with custom search? I am asking specifically about custom search and not views. I know that I could use views to do something similar but would prefer if this feature could be implemented as part of custom search.

Thank you