Boosters work in all servers, inculding public, private and user created ones...etc But once you reach the 100 game wins limit in a day, it won't work anymore until 24 hours from reaching that limit.
sometimes with boosters its a debate if they are worth it or aren't. you can get a booster for the 50tc + and up but sometimes you could buy the tc for cheaper and all depends on how much you work. the boosters are a fast way of getting TC if you're on a desperate need for it.
to say you could spend the 20$ for the 200 booster or you can buy 200k tc for that 20$. its a give and take relationship on what you want and how you will work to get it. just depends on what YOU want to do mainly.