Type-C port is engineered to be very "safe" in all aspects of interconnect. By definition, a well-designed Type-C port doesn't output any voltage unless the connect to cable (or partner device) is detected and port's power role is determined, either from the default CC pull-up-pull-down arrangement, and/or via Power Delivery communication. This also applies to any USB hub, self-powered or bus-powered.
In order to support normal USB connection via a video card (I assume a standard PCIe-based add-on card), the card must have an USB host controller embedded behind the PCIe bridge that hooks both GPU and xHCI to system's PCIe. You can check the presence of extra USB controller by looking into USBTreeView connectivity. But since the Gigabyte card says it supports "Virtual Link", the architecture of USB connection can be more convoluted.