Not in theory, but in practice you can play "offline". The only difference besides not having to have an account (so not having to pay) is that you can't join certain servers like Hypixel (which is a big deal for some players like me) and the scam that Realms are. Servers that allow non-premium players to join need, however, to add the AuthMe plugin that requires you to enter a server-specific passsword since anyone can login with any username otherwise. That also means that usernames are first come first serve on these servers, which can be an issue for impersonating, not to mention that hackers can just make new accounts easily. A solution you'll usually see is custom clients that make it difficult to change mods and inject cheats. I hope I gave you a pretty decent idea of the difference between premium and "offline" ^^
