peep The only difference between a custom game and a dedicated server for that matter is that when you host a custom game you are the host, when you join a server the server is the host
So for example mod menus will not work out of the box on dedicated servers, you'd have to specify which players it would give it to. For custom games since you are the host it would directly give it to you.
For scripts that don't have this kind of logic with hosts and such it works right away the same than it works in your custom games