You can run beer through stout faucet with CO2, but you won't be able to increase the pressure to optimize use of stout faucet.
Ideally you want 30-40 psi serving pressure with stout faucet. If you set this pressure with CO2 you will have an over carbonated mess. If you use beer gas (75% N2 / 25 % CO2) you can run at high pressure withou overcarbonating your beer, because N2 is not very soluble in beer.
At a minimum you will need a bottle of beer gas. No one should fill CO2 bottle with beer gas as they are rated differently. Next you will need a regulator compatible with that bottle which will have male threads. You can buy converter to work with CO2 regulator, but I recommend spending money on N2 regulator (again they are rated differently).
You'll end up with one setup for nitro and one setup for CO2. More expensive, but right way to do it.