It IS possible for a trojan to install mIRC. Damn easy even, it just has to get a file off the server, run said file, push some buttons. I could do it in VB even.
Its also possible to decompile mIRC, fix all the errors that always seem to happen when you use a crappy decompiler, then add in trojan/virus-like code. Which is why (or at least one good reason why) they tell you to download mIRC from this site and nowhere else.
(Its also illegal in a couple of ways, of course.)