My thought is "no."
Old site A is to be redirected to corresponding pages on new site B without altering the URL, that is, example.com/widget.html 301's to example2.com/widget.html.
The catch: there must be an interim message for users "why you have landed here" as a legal requirement.
It would be easy to do example.com/widget.html?f=a and use the query string as a hook in site B's .htaccess, but that changes the URL and you now have two pages, duplicate content.
Am I correct? Would this work without loss of indexing?