Yes, stand up pouches remain stable on store shelves. The design of stand up bags is such that stability becomes an inherent quality of these pouches. Stand up pouches have to be packed flat. Nonetheless, they are designed in such a way that when filled with a product, they remain bottom heavy. This keeps the center of gravity closer to the ground. An object with a heavy bottom is less likely to tumble over than a product with a light bottom. This is why standup bags stand erect on store shelves.
 
The Egyptians made pyramids with a heavy bottom and light top. An inverted pyramid would have been so unstable that a mere gust of wind could have destroyed it. Something similar happens in pouch bags where heavy products stay near the bottom and lighter air fills the upper parts of a pouch. The center of gravity goes down to even lower parts as the product is consumed. Therefore stability increases as consumers empty a pouch. An empty pouch, however, is not very stable because of its negligible weight.
 
When it comes to stability, pouches are even more stable than long bottles and jars. The underlying reason is once again a lower center of gravity in stand up pouches.