No, the buckets come off of a vertical bus, which attach to a horizontal bus across the top. The service entrance to the mcc can either have a main c/b or switch or be main lugs only. This depends on what is feeding it. Check your local/National El. code.
Most MCC's I have seen have internal bus and the buckets have stabs that connect to it. Every bucket I know of has it's own breaker built in. No matter if it is a motor starter or AC drive such as General Electrics MCC's
Generally speaking, NEMA Size 5 starter and smaller are connected via bus stabs, Size 6 and larger are cable connected to bus. MCC Buckets using MCP are HP sized.
MCC Buckets using Fuses are sized by HP range ie 20-50 hp.
You select branch circuit protection.
Comment: Some MCC compartments accept circuit breaker pannel (usually lighting and receptacles). One may potentially use these branch circuit breakers to protect other MCC compartments internal circuitry, in general. However, this appears to be very rare case; but it could prove to be a money and labor saver.