I'm not quite sure where the rumor that some schools are welcoming of students with undefined career objectives is coming from. That is simply not true. It is not true of Cornell, or any other school I'm aware of. While you don't have to necessarily cite a specific company you want to work for, you better be sure you know what you want to do post-MBA (or at least be convincing enough that you do).
If you don't have clear career goals, it's very hard, even impossible, to come across as an ambitious and focused person who will drive results (and those are the type of people schools want).
That being said, most people don't quite know what they want to do - that's a part of the whole learning experience (it's ok when you're here, not quite ok during the admissions process).
alwaysmiling, I'd suggest that you read up on both career options (Vault and Wet feet might be good sources) and see which one is the one you're more interested in. The trick is that you have to come up with a convincing enough argument - what is your experience so far, what portion of it can you transport to your chosen field and why you want to get into that particular field. It should all make sense, beyond that there are no right or wrong answers.
Regarding immersions, you're expected to declare an immersion in October, but that is not something you should worry about at this point. No one will hold you to whatever you wrote in your application. You can say investment banking in your application, then decide that the strategic marketing immersion is the right one for you, etc. Regarding your question on clearly defined objectives - most of my classmates have an idea of what they want to do but few of them are dead set on a specific path. You're expected to at least know what's out there, but no one expects you to know what you want to do for the rest of your life upfront (caveat: again you're off the hook only AFTER you get that admit call). That is not to say that the school is receptive of applicants who don't know what they want to do. You'll be well served to have a convincing argument about a specific career path. Your chances of getting into a decent school (ANY decent school) without having a clearly articulated career path are slim at best.
Feel free to PM me if you have specific questions about your particular background and how you can position yourself to make sure you have a story that makes sense - I'm happy to help as much as I can. Same for anyone else out there wondering about the same thing.