The Converse site no.  Right click anywhere on that page.  It's a Flash application.  No good for mobile or anything.  Really a bad move on their part by such a large corporation.

The Vans site is maintained by IBM Websphere Commerce platform: http://www-01.ibm.com/software/genservers/commerceproductline/ .

You can typically find out a lot about what a site is made of by viewing the source code.  If you do not understand the source code, jumping to DW will be a huge leap.

Asking if Dreamweaver can build a site is like giving you an unlimited supply of lumber, a hammer and some nails and telling you to build a house.  Some people could be a mansion with those while others might struggle to make a dog house.  Dreamweaver is a tool.  It is not a one-click solution to build those types of enterprise level sites.  It can give you the tools to make skinning a content management platform easier.  It can also make programming easier by giving you access to code hinting, code coloring and other features.  So just think of it as a tool and not a solution, because if you believe it is a solution you will be greatly disappointed.

The applications Nancy mentioned will give you a good start because the platforms those comapnies are using could be out of your budget financially.  Usually when companies don't even post prices to solutions online and tell you to call someone in sales, it's not cheap.

If you're going to be using Dreamweaver, you really want to look at using Adobe Business Catalyst because it is an all-in-one ecommerce hosting solution that has been nicely integrated into Dreamweaver CS6.

We've been using Business Catalyst for client ecommerce sites and I can't recommend it enough.  You don't have to learn PHP or SQL with BC. If you know HTML/CSS and maybe a little javascript you can do some really powerful things relatively easy because BC is designed to handle all the backend database functionality through simple modules and tags.   And the same way Dreamweaver does code hinting for HTML and CSS tags, it does for Business Catalyst's modules and tags for ecommerce and database functionality in CS6.

So with BC, basically all you need to know is the front end coding part of building sites and you can do ecommerce sites in Dreamweaver.  But like someone else said, Dreamweaver isn't going to build the site for you.  The tools are there but it is up to you to know how to use them to their potential.