The sent message to the player online will be highlighted in his private dialogue.If you send a message to a player offline, then when he enters the message will come, but will not be highlighted as new. And he certainly will not read it.
Hello!
Yes, this is improved in the A22 update which is going to be released tomorrow (16th May at 1PM UTC (4PM Moscow time)). The game will properly handle unread private chat messages. We've also implemented closing the private chats, and several other chat-related changes. Patch notes http://forums.atomictorch.com/index.php?topic=1317
Regards!