Can I use the USB 2.0 and 3.x channels simultaneously in a USB 3.x port?
Ranting, comment, do something else recommendation

meh. FTDI's "our FT-60x can't do an obvious thing, so buy two of our products" isn't sitting all too well with me. Frankly, there's devices that do exactly what you want: 


First load a USB controller firmware via USB,
then download a bitstream to the FPGA via USB3,
then communicate with the now functional FPGA at USB3 speeds.


The device I have in mind is the Ettus USRP B200/B210/B200mini… series. They use a cypress FX3.

You can find 


the schematics of these devices here;
the FX3 USB controller firmware here;
the host-side userland software (this all works over libUSB, so no
custom kernel-mode drivers) here, and
the FPGA image source code here.


answering your question

according to https://electronics.stackexchange.com/a/266990/64158 (and the author of the linked answer is really knowledgeable about USB3), yes, you can use a USB3 link without USB2 lines.

However, your host controller and OS need to be willing to consider the two buses separate, if you don't want to use a USB3 hub. In my experiences, that is unlikely to happen if your host is a PC or something similar

If you're, however, in full control of your USB stack (because, for example, you have an OHCI / xHCI in an FPGA at the other end of the link, acting as host), this might work.