No, eCart does not have a function for managing inventory, you would need to hand code this.
Managing inventory is tricky, especially in a situation where you only have one of the item, you would need to add a check just before the code that processes the transaction to make sure the item has not been purchased by another user between the time they added the item to the cart and got to the checkout page, and add another block of code to remove the item from the inventory after the transaction has taken place.
this is not code that we can offer support for though, if you would like help creating this functionality, I would recommend signing up for a premiere ticket where we could work with you in a one on one session to create this.