Do I need to test the desktop layout on mobile if there is a mobile layout?

I'm making a website and the site will have a fully fleshed out mobile version. I'm just wondering if, from a user experience point of view I should verify that the desktop mode works as well?

Some users might opt to use the site's desktop version instead of the layout specifically made for mobile. Do I need to see the extra effort of tweaking the desktop version to accomodate those users who choose to use the desktop version on a tiny screen, or does it automatically become a given that it might not work as expected with the desktop layout?