Shell accounts are usually, if not always, Unix so I would think it is impossible unless there was a way to run an emulator on the account. If there is a way to run mIRC from a shell I would be VERY interested to find out too.
There is an alternative, albeit more expensive than a shell account and that is dedicated Windows hosting. Though this is usually for websites. If money is no object, co-locate a Windows server somewhere and you could have what you like on it.
