To communicate to mIRC from your application you can use dde or sendmessage. For information on both, and how to communicate with mIRC, check the help file.
COM will be of no help for you, since COM is called from within mIRC whilst you want to communicate from an external program to mIRC. No you cannot communicate from DOS to mIRC. It is possible with COM to communicate with DOS, and return information from DOS to mIRC, but that means all code is processed on mIRC's side. That doesnt' seem to be what you're asking. You want to use a command in DOS and want it to appear in mIRC I suppose? That can't be done.
Note that the dde and sendmessage tips are for when you are developing an application, and wish to be able to communicate with mIRC. Obviously you cannot communicate with mIRC with an application that does not support this kind of features.
If you can program, which I assume you can, you can create a DLL, which can act as the intermediary between your application and mIRC, if for some reason dde and sendmessage are not sufficient for you.