As far as I know (which may not be very far
) the only way around that fatal arror is to have a MySQL server reply to the mysql_connect() call. I've never implemented another means of having MySQL function calls actually 'work' without MysQL installed.
I wouldn't put it past some very creative scripting though, for there to be a way around it. Php is a pretty powerful language. Perhaps in the Apache httpd.conf (or *maybe* php.ini) you could arrange to pre-empt or redirect the mysql call(s) to another page with a little script which simply returns 'TRUE' or whatever value/return-code would be returned by the mysql_connect() function?
I/we did this to implement part of a firewall on a Debian server a while back using Apache's php-prepend functionality. You might have the mysql_connect function call all alone on a page by itself, which when called would actually get prepended by apache and replaced by the script which would return the phony 'TRUE' (or error=0)
Of course, the php may be 'too smart to fool' so easily :P