Yes, you can follow the guidence here to move the databases: http://msdn.microsoft.com/en-us/library/ee378546.aspx
So long as the version of SQL Server is supported by the version of BizTalk Server, which SQL Server 2012 is, you're ok.
The process you describe is essentially staging a new BizTalk Group, database and all. If you don't have to maintain long-running Orchestrations, this is the method I would recommend and take myself in your situation.
I've done both and un-Configure/re-Configure is just easier.