No, it's not.
As explained by Hans-Hermann Hoppe, there's a great difference between the free movement of goods and the free movement of people. Goods have a willing sender and a willing buyer. That's not the case with people. Libertarians do favour immigration controls: by the owner of each piece of property.
I see today that the Labour party is saying that under independence:
Passport controls would be introduced at Gretna and Berwick to restrict the movement of people into England if Scotland voted for independence, the Westminster government has warned.Perhaps so, but this also implies that the movement of people from England into Scotland would be also restricted.
Once every piece of property is in the hands of its rightful owner we'll see just who is allowed to move where. But, in the meantime, I don't think that's it at all obvious that Scotland would necessarily be worse off than England in the event of border controls being introduced by governments.