The default functionality is to just insert the link like you mentioned. Mail clients will treat this differently, if links are not allowed making it into a standard html style link will not fix the problem. If links are allowed the url should be clickable, different browsers and mail clients will do this differently though. You could always add in some text to let the user know to cut and past the link if it is not clickable. This is a very common approach when sending email verification links.
When it comes to the problems you are having with the checkout please explain a little about the steps you are taking in your testing and the specific results you are getting including any errors.