Not necessarily. If you install a skin to replace an existing skin that you don't like then even if you play multiplayer you will see that skin on other players regardless if they have it or not. It must be available in the mission though.
Also if you decide that you will not replace and existing skin and merely add it and create a multiplayer mission with a skin of your choice, you'll see that skin in the game if you host but other players will default to the 1st available skin on the list, except for the ka-50 which will show orange (It's a bug that needs to be corrected)