Unfortunately not under the normal circumstances. Presumably, Valve's kang of Arch is missing one (or all) of the three dependencies (not sure how well the whole OS would fare without freetype though). I attempted to use the Steam Linux Runtime to no avail (it may require more work to run just any old Linux title).
The game provide the general "Failed to connect to local server" error. I may dig in with Protontricks and see what can be done to get around it in the meantime. I could also probably explore compiling the game in a Flatpak or AppImage, which Valve primarily recommends for running software in desktop mode