No your password will not be added. Oauth is the method used to connect to Gmail and it does not use your password, only a token issued by Google as part of your initial authentication. However Thunderbird never deleted anything from the password manager, so any legacy use of passwords for either IMAP or POP will see entries (not current if you have changed your password) remaining there in perpetuity.

I don't fully understand? So, when a Gmail account is added to Thunderbird, If you look at the saved passwords you will always see Oath for the email account, but you may or may not also see IMAP or SMTP in saved passwords (saved logins). Some gmail accounts will include the IMAP, SMTP or both in saved passwords (saved logins), but others won't. It depends on when the gmail account was created. Am I understanding this correctly? Also, if Oath always appears, but IMAP, SMTP or neither appear in saved passwords (saved logins) for a some gmail accounts. Does this mean there could be issues receiving incoming mail into Thunderbird for those gmail accounts, or issues with mail being delivered when being sent from those accounts with Thunderbird?

Thanks