I don’t know if that adapter and hardware is just a different wiring to PCIe, or if it has some protocol or other wiring difference. I suspect it is just ordinary PCIe with different connectors and probably it should behave just as normal PCIe…but I am guessing.
In the case of normal PCIe, regardless of whether there is a driver for your end device, there will be a PCIe listing from lspci if the control channel signal finds a device to talk to. This channel is not designed for high speed…it is designed for establishing parameters of the PCIe device. If the signal quality is too low then lspci would not show any device. Though I can’t be certain, this is probably an indication that signal quality has degraded even in the control channel.