Maybe you will, maybe you won't. It depends on what Apple sends you. If they send you a MBP Leopard disk, then it's unlikely (although still possible), while if they send you the full Leopard version, then almost certainly.
You won't know until you get it and give it a shot.
But either way, it's kind of illegal, whether you care or not is a different story.
Actually, I don't really understand where you're coming from. If you're going to illegally install the MBP cheap version on your other mac, you might as well install the cheap version on both. And if you're going to buy another version of Leopard as well, then there's no reason why you need to break any of the terms. The $10 and $130 versions of Leopard are going to be exactly the same...