No. You have to wait until the period ends, AND you have to cancel your subscription before that happens, otherwise it'd renew automatically for another month regardless of the last subscription type.
I also did sub through both website and steam accidentally, and had to contact customer support for refund.
The whole subscription is so annoying now. I don't get why we can't just subscribe every year like before, and use a single, unified account for steam and all sources, not "linked" this and that.