Sure, if the interior is kept below 0C. That's pretty hard for most coolers, which are, as the name suggests, coolers. However depending on the ambient temperature and if you used dry ice (frozen CO2) you could keep the pizza frozen.

A frozen pizza can stay frozen in a cooler, but only if you use a high-quality insulated cooler and the correct type of refrigerant. If you simply use standard ice cubes, the pizza will likely begin to thaw within 4 to 6 hours because ice melts at 0°C (32°F) and a freezer is typically -18°C (0°F). To keep a pizza "rock-hard" frozen for a long road trip or camping, you should use dry ice or high-performance "sub-zero" gel packs. When using dry ice, be sure to wrap the pizza in a layer of cardboard or a towel so it doesn't come into direct contact with the ice, which can cause "freezer burn" on the crust. Additionally, you should "pre-chill" the cooler by keeping it in a cool room or putting a sacrificial bag of ice in it overnight before you pack the pizza. The more "dead air" space you have in the cooler, the faster the contents will thaw; fill any gaps with extra ice packs or crumpled newspaper. If the cooler is packed tight and remains closed, a pizza can stay frozen for 24 to 48 hours. If the crust becomes soft or the cheese feels squishy, it has likely entered the "danger zone" for bacteria and should be cooked immediately or discarded.