Multisite Sub Domain Creation For Affiliates

Is it possible to create this Affiliate setup Wordpress with Multisite?

I would like to give new affiliates for our product based business a subdomain of our website (probably created with Pro Sites) that acts as their affiliate referral websites.

Example:

You would sign up at http://www.MySite.com for our affiliate program. The new affiliate chooses a name of "Sara" to be her affiliate name and it would create a new site with a subdomain at http://Sara.MySite.com. This is where she would send her clients to purchase products from her site opposed to the usual referral links of "www.MySite.com/ref=?Sara" or something of that nature.

Is there any way possible to do this out of the box? If not, what about with custom coding? I would like to keep it as automated as possible.