Yes, it works—but with major caveats. Satellite internet (HughesNet, Viasat, Starlink) can connect to CoD servers, but the experience differs vastly from fiber/cable.
Verdict: On geostationary satellite, CoD is functionally broken for multiplayer. On Starlink, it's playable but inferior to terrestrial broadband. If you have any other option (5G home, fixed wireless, DSL), use it instead.