I'm not a fan of adding markup to your HTML that cannot be seen and serves no purpose. You didn't provide a single benefit of doing that in your question and so the simple answer is: If you don't need a checkbox to be part of the page, then don't include it in your markup.
I suspect that a hidden checkbox will not add any noticeable time to the download or work by the server. So I agree it's not really a consideration. However, many pages do have extra content (comments, viewstate, etc.) and it can all add up. So anyone with the attitude that they will go ahead and add content that is not needed and never seen by the user, I would expect them to create pages that are noticeably slower overall.
Now, you haven't provided any information about why you might want to include markup that is not needed. Although you said nothing about client script, the one case where I might leave elements in a page that are hidden is when I'm writing client script to remove them. In this case, I may hide()
it and leave in the markup. One reason for that is that I could easily show it again if needed.
That's my answer, but I think you'd get a much better answer if you described what considerations you had for including markup on the page that no one will see. Surely, it must offer some benefit that you haven't disclosed or you would have no reason to do it.