Yes, it would, but there are cases of it not dying like an annual, coming up from root and seed. I believe I mentioned somewhere on this site that our county puts natives in the ditches, so I hope that if our plants spread at all, it will just add to that.
I do not want to bring anything into the area that could compete with the natives. I know it would not spread like in the more tropical areas.
Scroll down to "The Threat of Nonnative Milkweeds".
http://edis.ifas.ufl.edu/uw311