I'm not really sure about top programs. Here are some stats about Harvard's master's programs: http://www.gse.harvard.edu/masters/life/who-studies
Looks like master's students have work experience, but that includes programs other than MAT and may not be education-specific experience. I'd say read the profiles of admitted students that are listed on websites like STEP, see if you can find admissions statistics, and look through the threads of the schools you're interested in and pm people who applied to your programs. My guess would be that you'd need enough experience to explain/justify your interest in a MAT program in a statement/interview but not much more than that.
Just another thought: if you ultimately want to study policy or do administration, you may be want to consider doing an alternative certification program like Teach For America, Match Corps, or something similar. Plenty of people from these programs move on to policy and administration. That way you would only pay tuition for one program, so it would also be much more affordable. Tuition at top MAT programs isn't cheap, and as I understand it, you likely won't get much of a scholarship. I think having tens of thousands of debt may cause you to hesitate to get another expensive degree (e.g. ed policy) for the career you really want. You wouldn't teach German, but unless German relates to your interest in policy or administration that probably won't harm your long term goals. I did TFA, and it's certainly an intense experience, but it was great for me. It definitely offered insights that would be very relevant to policy and perhaps higher ed if you teach in a high school--particularly if you are interested in issues of access to higher ed.
Perhaps apply to those types of programs in addition to MAT ones to give yourself more options? You know your goals best, but I just thought it is something to consider!