Was curious if multiplayer allowed for LAN without needing to be run through Galaxy.

Yes, you can use direct connection or join games from the lobby without using Galaxy. I've attached screenshots of the game's multiplayer menus as accessible while just running the game from desktop, no Galaxy installed.

Thanks for confirming LAN! Hoping to pick this up during one of my paychecks :D

What about with Steam? Will it work cross platform?

Steam uses the same port so you could set a [public] multi platfrom up against a proxy server but not by default
your options are;
private
public
friends only