No. To expand, I am picking up some dropped domains, that have backlinks to deep pages.Do you know what pages are being requested (that cause the 404s)?
ErrorDocument 404 http://www.mydomain.com/optional-path-to-page.php
ErrorDocument 404 /404.php
<?php
header ('HTTP/1.1 301 Moved Permanently');
header('location: http://mydomain.com/index.php');
Yes, this. A+++You want to keep the goodness of the backlinks and bounce it to root so do you want to just 301 all the 404's to root? (Without showing a 404 header)