Hi,
This is the only place in the main chat window that says any account is Off line.

This is the box bottom left of the window.
It also give you access to the Status Messages that apply only to Buddy List Accounts (AIM, Jabber/Google, Yahoo and Bonjour)

It is very similar to the one from a Buddy list itself.

The only place in the whole app to "turn On" the iMessages account is here.

This item in the Messages Menu only works with Accounts that have Buddy Lists

There are situations where the Pane at Pic 3 looks very different if the account (iMessages) is not logged in and refuses to do so.
The Main chat window may show that an iMessage is about to be sent but selecting a Contact in the "To" spot turns it red or when sending an iMessages instantly displays "Not Delivered".
This example pic shows a Text (SMS) Number which goes green - Failure to login properly will show a Contact as red.

The original Poster implies that the Chat window looks normal but that the account says it is Off Line.
They are not clear where they are seeing this.
If the Account is not Enabled it looks like this

And the To Spot does not display iMessages Contacts as options.
If it fails to Login or your deliberately Sign Out it looks like this.

To be clear - Messages is the App. iMessages is just one account type and method of sending text based chats to Apple IDs and iPhone numbers that are registered with the iMessages service.
The iMessages account never says it is Off line.
It either fails to Login in the first place and tells you with a pop over the last pic or it reveals it only in actions you take in the Chat window.
It is not one of the accounts listed in the bottom left box.
As Buddy List account types and the iMessages account behave differently I did ask for what people are seeing and where they are seeing it.

10:18 p.m. Saturday; October 24, 2015
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