Hi,
In Addition for anyone else reading this.
The item in the Messages App Menu > Status does not do anything for the iMessages account.
Like many of the other menus it only applies to Buddy List accounts (Bonjour, AIM, Jabber/Google and Yahoo).
As the Bonjour is the only other Account that you cannot delete and is is there from day One it is by default Not Active and Off Line.
For this reason you may see the Menu Item set at Off Line.
This is the Setting in my Bonjour Buddy List

This is the Menu item.

As you can see there are minor differences but they are essentially the same thing.
The only way to check the iMessages account is Logged in is to do as Eric suggests (Preferences > Accounts > iMessages Account > "Enable this Account box") or to Send an iMessage.

8:33 pm Sunday; January 31, 2016
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad