If a fuse or circuit breaker directly opens a circuit when the current limit is reached, do overload heaters open and break the circuit when their current limit is reached?

No

Explanation:

No, overload heaters do not open to break the circuit when their current limit is reached. These are safety device to prevent over heating.

Thermal overload relays in a motor are intended to protect the conductors (windings). Such safety devices are made to maintain the current flow in a circuit at a safety level so as to avoid overheating of the circuitry conductors. And the excess of current is often called as over current.