No, since copyright exists once your create a new creative work, so you would have copyright in your designs; copyright would preclude them from using, reproducing, etc. your designs without your permission. That's the law; factually, it can sometimes be hard to prove you came up with the design first, so you probably should not send in unsolicted designs, but rather first corresond with the company and determine the submissions process (and review any paperwork, forms, etc. they want you to sign carefully!), so as to be able to better prove that you came up the designs and sent them in for review at their request/invitation.