No. It's a fact that we teach children to wear clothes. We do not know what children would do in the absence of any instruction, or if modesty might manifest without an example. It would be unethical, if not impossible, to find out. Seriously, think what kind of experiment would be required to test this hypothesis, and then think about what an IRB would say to its proposal.
But it's also probably irrelevant. Let's suppose that clothing is socially indoctrinated. So what? That doesn't make it arbitrary or useless. As I said before, I think clothing is necessary for mixed sex strangers to be able to interact with little social friction. If I am correct, then even if clothing is a complete social construct, then it's still a necessary one in modern society, and we should not try to get rid of it.