Yes, a number of baby food pouches are designed to bear significantly higher temperature than the typical room temperature. So they can be easily stored outside a refrigerator at room temperature. The packages that can be stored at room temperature include foods that do not rot or spoil without freezers. For example, you should not store frozen meat outside the freezer. It is best to get the storage information printed on the bags of food so that the customers can be certain.
A baby food pouch that contains ice cream, frozen fruit pulp, or other items that require low storage temperatures are best stored in freezers. They may or may not spoil in the heat of a room, but they can become un-consumable. Very few people will like to eat melted ice cream, or chocolate that has turned into a cocoa paste (although it might still be fit for consumption). So even though most stand up bags are able to withstand room temperature without any damage to their structure, this may not be the case with the food they are carrying.
A class of stand up pouch bags used to store baby food is designed to bear temperatures of close to 100 degree Celsius. This is much more heat than possible under natural circumstances, even in the Sahara. Other stand up pouches for food packaging may not be so well designed.