According to the USB-C Spec:
Successfully entering an Alternate Mode may be predicated on only one of the available modes being successfully recognized by a host. In this case, the device is not required to expose but may still expose a USB Billboard Device Classinterface to indicate to the host the availability and status of the modes it supports.
The host may send an Enter Mode after tAMETimeout. If the device enters the mode, it shall respond with an ACK and discontinue exposing the USB Billboard Device Classinterface. The device may expose the USB Billboard Device Classinterface again with updated capabilities.
So if I'm reading this right, exposure of the USB Billboard Device Classinterface is optional after Alternate Mode has been entered. Unless I hear differently, this is what I'll assume is the case.
Your understand is correct.