Tony, are you talking about something like this?
Not sure just yet. It depends on how that applet works.
If it's a java applet which is merely a java replacement for MIRC (in other words, the communication still happens with your local machine using the IRC ports that get blocked by firewalls), then no.
If it's a front end that uses HTTP to communicate with the chrismyden.com server and then something on the
server talks to the IRC servers using the "naughty" ports, then yes.
Can't tell right off the bat which of the two this is. I suspect the former.