Well, not if you talk to the shopkeeper first. Heck his sister even takes you outside and tells you exactly how to get there. The robbery is also mentioned by NPC's before you even go into the store. So I'm pretty sure you are guided to hit the Barrow first, then Whiterun. Granted, you are also told to go to Whiterun to tell the Jarl about dragons. So I guess it could go either way. How pressed are you to go talk to a Jarl right after you nearly had your head chopped off? Also the Barrow is pretty much scaled to a low level character.