Will related search words show on our website?

Hello.

I have no idea if you can acutally see the pictures that I’ve uploaded.
I want to know, if I upgrade to Yoast Pro – mainly because of the Add Related Keyphrase section. Will all my Related keyphrases be searchable in my Ajax search plugin-function on my website.

I have this machine called one thing (rillesk?rer), but out in the everyday-workers-field it’s called something else (rillefr?ser) – and some of them will search for the nickname of the item. I need it to be visible on both names. Is that possbile with Yoast Pro?

The only reason why it’s working now, is beacuse I’ve enabled “Short Description” as an searchable field on my website – and therefore I need to add a line in my descriptopion “Also known as …” I want all that to be backend, and not visible on the page.

The page I need help with: [log in to see the link]