Can i play on Premium servers?
You can play on premium servers if you own Mojang account or if you're using some sort of alt system like McLeaks. In most cases those launchers only allow you to play on non-premium servers.
If server settings are set as "online-mode=true" only premium/loged in players will be allowed. If server is set as "online-mode=false" it will allow premium and non-premium users in.
Wondering why you can't join as you're already in the game?
Launcher is only loading the game, the first step of login in is only checking if you own game, if this step is skipped you will be able to play Singleplayer. But as soon as you try to join a premium server, it checks again and if you're not premium you won't be able to play. Now you're probably wondering why cracked servers can work then? Every server has option called "online-mode=" it can be set to true or false. If setting is set it to true it means the server is premium and "game" will check if you're logged in or not. If setting is set to false, user can join even if login process was skipped (checking process is skipped). Now you're probably wondering why such option is there? Maybe someone wanted people to play for free? Or not? This is a simple explanation if you're wondering how it works Google will help.