Does broswer load the same template twice?

I have a login form with lots of user profile data in sidebar.
I don’t have sidebar on front page, So I created a user.php for the login form and use get-template function to call this user.php on front page.

I guess the same login form is loaded twice– one is coded in sidebar, another is called from the user.php on front page.

Maybe I should replace the login form in the sidebar with the get_template function calling for the user.php ? This way, the same code is loaded only once so that improve a little bit performence?

If my guess is correct, I will implement this idea on several part of my blog. If browser loads the same template every time it being called disregarding it is the same name, then, I don’t need bother.

Need your opinion!
Regards