First your connection string will look something like this:
<add key="[keyname]" value="user ID=[username];password=[password];data source=[servername|ip address];persist security info=True;initial catalog=[name of database]"/>
Second, yes you can leave the connection string you provided in your post intact and just add a new key in the config file. You will just need to point at the SQL Server key when the site is live and at the SQLExpress key when its on your Dev box.
I will only tell you how to do it, not do it for you.
Unless, of course, you want to hire me to do work for you.
^^Took that from planoie's profile