Hey @Hadar Blutrich  Shauna here from Intercom Support! 

You can disable the ‘chat function’ on the messenger by going to Messenger Settings > Conversations > under ‘Control Inbound Conversation Volume’ here.

You need to turn off the following option for BOTH users & visitors

Once this is turned off for both users & visitors - the messenger will still be live but customers cannot open a conversation. I hope this helps