I want to have a link that includes a query string to enter my email so that I'll be directed immediately to the password textbox. Is that possible? (I want to click the link, enter my password, and click enter.)
It doesn't look possible. Even if you use the technique offered in this answer on a different (but related) question, and create a link that points to:
https://mail.google.com/mail/u/?authuser=user@gmail.com
You'll still be prompted for your username before you're prompted for your password.
I expect that this is to add extra security to your account.