This may be a ridiculous question, but, can a secure (https) web page be optimized?

I have a client who just added a page to their site where they can start selling some of the products. They're not really an ecommerce site - just added that option/component.

They'd like to have it optimized so when someone is already looking for their brand, their "store" page shows up in the search results.

This store page is an https /secure page.
I"m assuming that's going to be a problem - as far as getting that page to appear in the search results, because I don't know that search engines show secure pages in the results. Do they? Can this page be optimized?

Please advise