Can drivers?
Yes. Most Windows (and Linux and Mac) drivers run in kernel mode and have full access to the operating system, including the parts that store the list of drivers. They can erase themselves from that list (and similar lists) and still continue to operate. It would have to be done on purpose, maliciously.
Plus, Device Manager shows devices, not drivers.
Plus, the driver is the one that knows whether the device is enabled! It could pretend to Windows that the device is disabled, while actually it's enabled and transmitting spy data.
"forest" mentioned in a comment that some hardware can be turned off. Of course even a driver can't use the hardware if it's turned off. I strongly suspect the driver can turn it back on without Windows noticing.
Can firmware?
Yes. Except if the device with the firmware is turned off (as pointed out by "forest"). If your wi-fi card is turned off (no power) then it doesn't matter what firmware's on it. If it's turned on though, it can do evil stuff. If it's different firmware that's infected (like your BIOS/UEFI) then it can turn on the wi-fi card and then do evil wi-fi things.
Firmware doing evil wi-fi things and drivers doing normal wi-fi things would be likely to clash with each other and cause the wi-fi card to stop working properly, so it's not likely, but it's possible.