Yes. A FB business page like sticks, as does a like of a page on your website. The latter is far more desirable I think contrasted with someone liking a FaceBook post or page as that is digital sharecropper property.
Hmmm, I've got quite a few page likes on my website, but haven't seen any indication that posting to my facebook business page has any type of viral affect centered around the people who pressed the "like" button on my website.
Do you have to do anything special to tie your website likes to your facebook business page?