I'm responding to your question as a former Director of MBA Admission, a position I held for 15 years at a top-ranked MBA program.
The only definitive information a school can see is the list of schools you sent your GMAT scores to. This appears on the school report of the GMAT scores, which has slightly different information than the student-based score report.
Now, even though I could see that list, it doesn't mean anything really unless a candidate has actually applied to those schools. And that is something that is not known.
Another way I might be able to tell if an applicant is applying to another school is if they made a mistake in their essays and put the name of a competitor school in the essay. Humorous, yes. This happens very frequently. It's not a reason to deny an otherwise qualified applicant.
One last way I might be able to tell if an applicant is applying to another school is if the recommender sends a recommendation form for another school to us. As the recommendations become more web-based, this is less of an issue. However, when I was the Director of MBA Admissions, I always instructed my staff to forward those letters on to the correct school as a matter of professional courtesy to both the applicant and the other school. I can't say what the policy of other admissions offices was.
As an admissions professional, I found it interesting to discuss the school choice set with the applicants, and would always bring this up in my interview. I also always asked candidates which school was their top choice. What I was looking for in this line of questioning is not for applicants to tell me that they loved my school the best - but I was assessing their professional judgement and checking to see if their professional post-MBA goals lined up with their school choice set. I also expect good candidates to apply to more than one school. I think it would be very foolish indeed to apply only to one school. Why put all your eggs in one basket?
To get to the heart of your question, would this information count against you in your application? No.
However, this is a very common fear of applicants. In fact, applicants have many similar fears that appear throughout the application process. I refer to it as the "Urban Legends of Admissions."
Some examples of other "Urban Legends of Admissions" include: I'll have a better chance of admission if I have an alumnus of the program write a recommendation (not true); if I'm admitted off of the waitlist, I'm a "second-class" admit (not true); and if I don't need financial aid, the program will be more likely to admit me (not true). No one can ever point to a solid source of of the urban legend; they just know that they've heard it somewhere. (Hey - maybe I should launch a Snopes site for the Urban Legends of Admissions!)
If you have questions like this that you don't feel that you can pose to the admissions team of the schools you are applying to, you are welcome to send them to me directly. I'm happy to share my information and insights from my years of experience in this field.
I hope this helps. Good luck on your application process!
15 Years as Director of MBA Admissions - Now Working For the Applicants as the MBA Admissions Coach
Wendy Flynn is the MBA Admissions Coach, providing comprehensive MBA admissions consulting services. As the former Director of MBA Admissions for 15 years at a top-30 MBA pgoram, Wendy holds deep expertise in admissions issues for Full-Time, Executive and Professional (Part-Time) MBA Programs. Through her blog, MBA Expert Insights, she brings the view of the Director of MBA admissions to MBA applicants and others.
MBA Expert Insights Blog: http://www.mbaadmissionscoach.com/blog/
Member of the AIGAC, Association of International Graduate Admissions Counselors