About TI's DC/DC Converters Protection Question

Generally speaking no. Cycle by cycle current limit limits the current on each switching cycle. For normal peak current detect, it has the effect of lowering the duty cycle, so the output voltage tends to reduce while the current stays at the current limit level. Hiccup mode current limit will cause the converter to shut down and restart when the current is above the limit. It will continue to restart as the fault is present.
All that being said, it is common to have a mix of both types. In one case you may have cycle by cycle along with under voltage reset. As stated above, cycle by cycle current limit will tend to reduce the output voltage. If the output voltage falls below a certain threshold the converter will restart. This is effectively the same as hiccup mode current limit. Another frequent implementation of hiccup mode is cycle by cycle current limit with a counter. If for some preset number of consecutive switching cycles cycle by cycle current limit is detected, then hiccup mode is activated.
This is just a few examples of common implementations. Others are possible.