Can Fchat send mass messages to all old customers?

Absolutely YES! 

Mass messaging to old visitors is one of Fchat's most outstanding features.  Fchat sends messages with one of the three allowed Facebook tags including CONFIRMED_EVENT_UPDATE, POST_PURCHASE_UPDATE and ACCOUNT_UPDATE 

To send mass messages to old customers, you first need to synchronize customers. Go to Dashboard >> Customer >> Synchronized customers 

After synchronizing customers, you can send mass messages to them at Campaign. 

You can see instructions for sending the campaign at: