No. The virtual machine will always have an open IP address. But you can not assign Endpoints (leave the VM without any endpoints) - this effectively blocks all and any Internet traffic for your virtual machine before this event reaches the network of internal data centers.
There will always be a public IP address assigned to a cloud service with something deployed. It is up to you to decide whether to allow Internet traffic to your virtual machine or not. And this decision is made by defining the end points.
EDIT
Using Azure Resource Manager, you can create a virtual machine without a public IP address. You can control this parameter in the network adapter. In the IP configurations for the network adapter in Azure Resource Manager, you specify NONE for the Public IP Address parameter.