Not that I know of. The wp-login.php file is almost 700 lines of code. It handles a lot of authentication and other functions, to protect your blog. By comparison, the search function is relatively simply.
On the other hand, it is relatively easy to insert a link to the login page just about anywhere, using action hook widgets, although that’s not really what you want.
You might try searching the plugin repository. I did a cursory search and didn’t find much, but there may be a plugin that will do what you would like.
Good luck,
Ken