mIRC uses OpenSSL, which supports the "empty fragment" feature (first introduced in 0.9.6d which was released way back in 2002). It is possible to disable this feature however, so we'd have to hear from Khaled whether this feature is left enabled or not.
You can read a little about this feature here: http://www.openssl.org/~bodo/tls-cbc.txt (item number 2)
In short, if the "empty fragment" feature is enabled (which it is by default), then SSL connections created by mIRC would NOT be vulnerable to the BEAST attack.
