Confirm to permanently remove your answer!
The short answer is yes. However, you should not charge your cooler to the design pressure as it will be set off by the pressure relief valve.
The target pressure for the cooler or any particular pressurized equipment should be set to the project's operating pressure which is usually 10-25% lower than the design pressure.
Refer to the below link to an answer regarding working pressure and design pressure.
Hope that helps.
See additional pressure descriptions for comparison.
Maximum Allowable Working Pressure (MAWP) - maximum gauge pressure permissible at the top of the equipment in its operating position …