I'm not sure if this is a bug, but when checking
Options > Display > Options > Tray > On startup minimize mIRC to tray
When I start mIRC I double click on the icon in my system tray (as soon as it shows). mIRC opens but has about a 5-7 second delay.
Tested on mIRC 6.21 and 6.2 on WinXP Home (SP2).