I'll leave it to others to address the question of canon law (and you might try looking here
http://canonlaw.anglican.org/ } but the question of the civil effect of such a ceremony would likely vary from state to state. (One issue - does the state in question recognize common law marriage?)
You probably need to consult both a priest and a lawyer.
I don't know the answer for this particular church, but I'm glad people are starting to ask these questions. If the Episcopal Church won't do it, think about switching to a church which will.