At this time we do not support domain-specific SSL certificates for the full website. Currently, only customer account and Online Store secure checkout pages have SSL by default. The SSL certificate protection for these portions of your site is provided by VCG and is included in the cost of your store plan.
We do understand the importance of having SSL on all website pages with sensitive information. This has certainly been a discussion and we are considering ways to make this feature available in our next WSS update (website service).