That's not exactly the way to do it. Doing it the right way would involve making a Win32 application rather than an application that uses the DOS window (or whatever it's called) so that your program could run in the background. I'm not saying anything more than that, though.
Of course it is possible. But it is the Wrong Thing to do -- in computer terms, it is immoral.
Consider: you click on your web browser because you want to explore the internet. How do you think you would like it if Johnny Programmer decided that his program should also run when you start your browser? You would want to find J Programmer and nail him to the wall with the memory pins from his computer.
The correct way to start a program is because the user has asked you to run it.
Have the user start your program, which starts MS Word as part of its operation.