It seems my Coleman furnace relies on the hi-limit to shut down the burners, then when the hi-limit resets itself, the sequence of operation resume until the thermostat is satisfied. Is this normal operation?
An "upper limit" or "high limit" in a forced-air furnace is generally intended as a safety device, not for ordinary use to stop the burner. The thermostat controls of a properly designed system will only stop the burner when the room temperature reaches the desired temperature. In other words, the furnace should run constantly, with fan air-flowing, until the thermostat shuts off the burner.
The fan may have a dirty filter, closed registers or other obstructions that restrict the airflow and trigger the safety of the upper-limit switch. The system may be too large for the target living spaces. A gas-fueled fire may be burning overly hot for some reason. A good technician may assist in pinpointing the exact cause of a high-limit problem.
In many systems, such switches require a manual reset and can only be reset once without knowing additional "magic", to avoid untrained homeowners from bypassing the built-in safety.
In a word NO. The furnace should not shut down on the high limit switch unless the high limit is going bad or is the wrong one. High limits are usually set at about 200 degrees F. If it is cycling on the high limit then the fan is not moving enough air through or past the heat exchanger. The fan speed needs to be increased or any other thing that will move more air through the furnace