I can be totally wrong here (I’m into MODX - not into servers much
) - but FastCGI is the extension that allows PHP to access files without making them world writable right?
In that case you should definitely be able to run it without, though you are more likely to get folder permission errors (ie PHP unable to work with FTP uploaded/modified files unless world writable and the other way around).
Just checked - two Revo installs running on a simple shared server do NOT use FastCGI, while the server I put the rest of my sites on do have it.