What if I use a USB A - to - USB C adapter cable, with the A side plugged into a USB 3.0 Type A receptacle, and the C side able to accept a slave device, say perhaps a USB C flash drive. Will the C side of the cable still be rotationally symmetrical, as would be the case for using type C USB 3.0 throughout? My guess is no, because there are no CC pins on the Type A 3.0 connector, and only one set of Tx and Rx pins.
The Type-A receptacle doesn't have CC pins, it is true. But the CC pins are present in the other end (Type-C) cable. The A-to-C adapter you described is called "legacy cable assembly", where the Type-C end represents host functionality (because Type-A receptacle is normally a USB host). To make the Type-C cable end to look like a host, the C-end includes a 56k resistor pulled to VBUS. The resistor is mounted inside the Type-C overmold. This signals to a Type-C device that a standard 500/900mA host is behind the cable, and everything works, in both orientations.
Yes, it works. There is a CC pin on the USB-C side of the cable, and the cable connects it to VBus through a termination resistor (as the host device would do for a C-to-C connection). This lets the downstream device know its intended role, as well as the orientation of the cable.
If a USB 3 cable with an A plug and a C plug is used, then it is up to the device with a C socket to determine the orientation of the cable and perform usb 3 signaling on the appropriate pins.
Adapters with C sockets are not allowed by the standard, if someone was to make such an adapter anyway, then you are likely to find that superspeed only works in one orientation (or doesn't work at all).