"This site has the old CMS without the live editor. So do I just transfer the site as is and then upgrade?"
Yes, you could do that.
Your friends over here at WebAssist! These Dreamweaver extensions will assist you in building unlimited, custom websites.
These out-of-the-box solutions provide you proven, tested applications that can be up and running now. Build a store, a gallery, or a web-based email solution.