Short version: probably not. Most emulators don't support networked multiplayer.

If the game natively supports LAN play on PC, like Minecraft or Among Us, then yes, it's possible to connect a Steam Deck to other machines via shared wifi or an ad-hoc network.

However, if the game was designed for a custom multiplayer protocol, like a GBA or 3DS game, then you're out of luck. There are rare exceptions; some games are so popular that they have mods for network play, such as Project M for Super Smash Bros Brawl. But outside of those rare exceptions you cannot play emulated multiplayer over a network.