No answer in 23 minutes? Wow indeed.
Are you saying that you'd want your page to behave as if you didn't reload the page when you reload it?
Other than that, document.getElementById can return null (or if it was undefined). However, if it does return an input element of type text, its value can never be null - it is always a string. It can of course be an empty string.
Strings do not support addition, but they do support concatenation, and incidentally the same operator (+) is used.