Well if you have no draft mailbox list in the Mailbox folder, then it's obvious that it's not creating one for that account or any other, meaning it's putting the drafts in the IMAP draft folder. You may have some corruption within the Mail folder or preferences.
Try this out:
Select the draft folder under that gmail account in the sidebar, then go to Mailboxes in the menu and select Use This Mailbox for: drafts. That should move the draft folder from the gmail folder to Mail's main draft mailbox.
Open Mail's preferences and check to see that the box to store messages on the server is checked.
Create and save a test draft message. Verify that it's also saved at the gmail website (should also appear in the draft folder under gmail account at sidebar bottem). Once that's done, go back into Mail's preferences and uncheck to store drafts on the server. That should move the draft mailbox back under the gmail folder. Save the changes.
Quit and restart Mail and verify Mail's preferences remain unchecked for storing drafts on the server.
Create a new message and save as draft. Verify that it is not saved to the gmail draft folder in the sidebar bottem or gmail website.
If all's OK from there, delete the test drafts you created. Once again highlight the Inbox and quit Mail. Restart Mail and the draft folder should not appear in the sidebar. It will still appear on the toolbar if you have it showing (to show, select Show Toolbar in Mail's menu under View).
Create a test message and send. See if that works. Hopefully, it will fix whatever preference files is stuck.