If you completely delete your Microsoft account, it's gone and can't be used even to sign in to Windows.
If you are sure about this and really want to delete your current Microsoft account's outlook.com email address, yet would prefer to continue signing in to Windows with a Microsoft account, you should do this:
Switch to a local account (tutorial
Switch back to Microsoft account (tutorial
), this time entering your Gmail address as existing email:
Your Windows user account remains intact, all your files and apps will still be there. Only difference is that your new Microsoft account is using your Gmail address and if you want to you can now delete the original Microsoft account's outlook.com email address..