Yes – but that does not mean WordPress will convert that page to a results page. WordPress has it’s “results page archive” handler, and it is triggered whenever the “?s=” query argument is triggered by default. That automatically calls the proper theme layout file and prints whatever is in the results loop. A custom page is only a custom page, it will not become the results page, WordPress will not recognize that. The best way to get around it is to simply make changes to the actual results page template.