This is somewhat related to the old difference between a "modem" and a "winmodem": proper telephone modems performed the de/modulation internally, winmodems did not and relied on the host processor to do so, resulting in generally lower performance but a much cheaper device. At modern network data rates it is not really feasible to do this and the general direction is towards offloading more and more of the work to the network adapter, outside of the host's control or view.
For gnuradio you need raw radio samples, often referred to as IQ data due to the nomenclature for amplitude and phase. Few devices that aren't specifically designed for software-defined radio use expose this data because it requires extra complexity in the device and tends to be rather high-bandwidth. The "RTL SDR" TV tuner dongles are so well known precisely because they contain an undocumented feature that allows a host to request raw IQ data, although at a poor sample rate and bandwidth since these devices were not really intended for it.
The only project that so far has managed to even partially use wifi hardware as a more generic SDR is nexmon[1] and even that is rather involved. Really cool project but not much heard since 2018.
For just experimenting with modems across a noisy path one could just use the built in microphone and speakers.
1. https://github.com/seemoo-lab/mobisys2018_nexmon_software_de...
For my own use (on windows 10), I used the following device names for the microphone / speaker: Microphone: "Microphone Array (Realtek High Definition Audio)" Speaker: "Speaker/HP (Realtek High Definition Audio)"
Specific names on windows can be found in the Control Panel > System > Sound (as of the date of writing)
Once you have basic understanding of the topic, you can get better hardware: AirSpy (the same features as rtl-sdr, but MUCH better signal-to-noise ratio and bandwidth) or bladeRF (costly, but probably the best radio you can get now). For example I'm now building a weather radar based on bladeRF. The bladeRF has a FPGA with open-source HDL, so you can mess even with absolutely lowlevel and bleeding edge stuff.
Going back to your original question:
Most cards load firmware from a file when they are initializing (check "dmesg|grep firmware", on my machine, for example, it says it has loaded /lib/firmware/rtl_nic/rtl8153b-2.fw), you are free to modify it. However, all (or maybe almost all) wifi cards have the format of the blob completely undocumented so it would be very hard to make a modification that would allow you to transmit/receive arbitrary signals. Something similar has been achieved with GSM phones (see OsmocomBB), but it requires very complicated reverse-engineering.
Recently, there was a wifi stack released for a SDR, so the other way around: https://www.nuand.com/bladeRF-wiphy/.
In the US and other countries, it is to the best of my knowledge legal to modify firmware for hardware you own. The illegal part is broadcasting, most bandwidths are highly regulated. Listening on the other hand is mostly legal, or at the very least extremely likely to fly under the radar.
Few years back there was danger of FCC de facto banning alternative router firmwares like openwrt to prevent tampering with the wifi cards firmware.
This was the "only manufacturer signed firmware allowed" thing that thankfully was avoided.
FCC's motivation in this is to prevent people from using too much power or certain frequencies.
And as most manufacturers want to be able to sell in USA, it would have likely affected all versions. Kainda like how many wifi devices sold in Europe only go up to channel 11 on 2.4GHz, when the EU band goes up to channel 13. But ch12 and ch13 are not legal in usa, so they are blocked.
https://github.com/chunkeey/carl9170fw/ https://github.com/qca/open-ath9k-htc-firmware http://netweb.ing.unibs.it/~openfwwf/
Also note that it’s easy to break FCC regulations and generally be disruptive if you mess around with this stuff and don’t know what you’re doing, and the FCC happily hands out five digit fines.
https://github.com/seemoo-lab/mobisys2018_nexmon_software_de...
https://github.com/chunkeey/carl9170fw/ https://github.com/qca/open-ath9k-htc-firmware http://netweb.ing.unibs.it/~openfwwf/
No. There's a LOT of stuff the wifi chip does to convert EM to data, including despreading and other computationally expensive operations.
Using an expensive SDR, you can follow this paper from 2013 to see the block diagram of what decoding wifi looks like:
https://conferences.sigcomm.org/sigcomm/2013/papers/srif/p9....
https://www.rtl-sdr.com/receiving-ads-b-jetliner-traffic-wit...
https://www.theverge.com/2019/11/26/20981630/raspberry-pi-pi...
That seems like it would be a nice cheap one-two punch for getting started. AFAIR wifi uses the public (unregulated) bands so there should be lots of interesting stuff on those frequencies beyond wifi signals.