Normally yes, but IMAP accounts can bypass that in some ways.

Matt said

Normally yes, but IMAP accounts can bypass that in some ways.

My Account settings are set as "IMAP" This I am told is better than POP, correct? So how do I know whether the log out is being bypassed?

Google POP vs IMAP and decide what is better for you.

Some IMAP servers push new messages down as they receive them. They do not wait to be polled by the client.

You do not really log into or out of email servers. You ask for new messages. The server asks for your password. If provided and correct you get your messages. No real logout. The connection just ends.

Airmail said

Google POP vs IMAP and decide what is better for you. Some IMAP servers push new messages down as they receive them. They do not wait to be polled by the client. You do not really log into or out of email servers. You ask for new messages. The server asks for your password. If provided and correct you get your messages. No real logout. The connection just ends.

How I've got T. Bird set, as IMAP, I do not have to ask for new messages by inputting password, they just arrive. So does this mean I've got a IMAP server that pushes messages down as it receives them?

Did you tell Thunderbird to remember your password? If so it enters it for you. If you are using Gmail with Oauth authentication Gmail issued and saved a token that is used instead of your normal password. I have no idea what provider you use so no sense in guessing.

Contact your provider for questions on how their server works.

Many thanks for all advise