Hi,
If you settings are this:-

Then when the computer goes to Sleep a prompt to the Servers for Buddy list (Google or other Jabber server) is not sent.
Other people cannot see you as Off Line.
As far as they are concerned your Status is the same.
If the second line is set as in the picture then when you come back the app should appear to be open and On Line again.
You should not see the Window to Ask you what to do and you should not see any window suggesting the App is playing catchup to reset the Status or Available.
I say Should.
As I said above it relies on the fact that the setting is written to the .plist involved.
If you go to the folder ~/Library/Messages and then use the View Menu and then View Options and select show Modified column you should see that the chat.db items have dates and time that match when the App was opened (or the last message was sent):-

If they have not changed then the app is not writing to the File properly.
In ~/Library/Preferences then the com.apple.ichat.plist should also have today's Date when the app started up.
If you change the setting then the Time you did this should show:-

It this does not change then the .plist file is not being written to.
As I said as well the Read and Write route is via ~/Library/Containers/com.apple.iChat/Data/Library/Preferences and the relevant Alias

The Path/Route to the Aliases are shown in the blue box.
The iChat.plist Alias is indicated by the red one and the Arrow denoting it is an Alias file is also indicated.
It is because this App is a Sandboxed one (which protects the system if the app fails) that you get this convoluted Read/Write path.
I hope that is clearer.

8:27 pm Thursday; April 26, 2018
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)