Yes! For the newest update of Facebook Messenger for iOS 7, you just have to go to the message then swipe to the left on your conversation, click the "more" option and simply click "Mark as Unread".
The redesign version of Facebook Messenger iPhone app in the App Store for iOS 7 has also reshaped the profile pictures which are now circular like and it also uses a brighter color scheme that comes close to mimicking the look of Apple’s Messages app. The badges now also appear over a friend’s picture when they are on messenger making it like a typical chat app.
To mark a message unread in Facebook Messages mobile:
Tap the menu button near the message's top.
Select Mark Unread from the menu.
To change the read status for a conversation to unread in Facebook Messenger:
Swipe to the left over the desired conversation.
Tap More.
Select Mark as Unread from the menu.
Facebook Messenger has to be one of the most useful messaging apps you can get for the iPhone, purely down to the large user base that it comes with. Find out more at techradar.com.