Agreeing/expanding what has already been said, I don't think FastCGI will solve the problem.
Apache
Each request into Apache will use one worker thread until the request completes, which may be a long time for COMET requests.
This article on Ajaxian mentions using COMET on Apache, and that it is difficult. The problem isn't specific to PHP, and applies to any back-end CGI module you may want to use on Apache.
The suggested solution was to use the 'event' MPM module which changes the way requests are dispatched to worker threads.
This MPM tries to fix
the 'keep alive problem' in HTTP.
After a client completes the first
request, the client can keep the
connection open, and send further
requests using the same socket. This
can save signifigant overhead in
creating TCP connections. However,
Apache traditionally keeps an entire
child process/thread waiting for data
from the client, which brings its own
disadvantages. To solve this problem,
this MPM uses a dedicated thread to
handle both the Listening sockets, and
all sockets that are in a Keep Alive
state.
Unfortunately, that doesn't work either, because it will only 'snooze' after a request is complete, waiting for a new request from the client.
PHP
Now, considering the other side of the problem, even if you resolve the issue with holding up one thread per comet request, you will still need one PHP thread per request - this is why FastCGI won't help.
You need something like Continuations which allow the comet requests to be resumed when the event they are triggered by is observed. AFAIK, this isn't something that's possible in PHP. I've only seen it in Java - see the Apache Tomcat server.
Edit:
There's an article here about using a load balancer (HAProxy) to allow you to run both an apache server and a comet-enabled server (e.g. jetty, tomcat for Java) on port 80 of the same server.