I'm not a current student or alum of any program in the top 20, but for whatever its worth:
- You should apply to Yale if you find the program appealing. It takes 10 minutes to find an email address of a current student or to call up admissions to ask them to put you in touch with one. Another 10 mins to write an email asking for an appointment. 20 minutes to look up information about the program on the website. 20 minutes on the phone with a student or alum. This hour invested will give you real returns rather than a furball-hurling discussion on reputation vs ranking.
- I keep hearing a lot about Yale from the POV of nonprofit, but have heard they place students in finance and consulting too at the top firms. There may be other program strengths I'm not aware of, because I haven't looked into Yale's MBA in any detail.
- What matters most about an MBA (aside from the obvious goal of education and building relationships with classmates) is your first job out of the program. After that, employers will be most interested in knowing what you did at your last job and how it enables you to do best what they want done. Brand matters, but not nearly as much as your position out of the MBA and your networking skills after you graduate.
- Your school options narrow or expands depending on what you're wanting to do right after your MBA. Want to do operations or general management? Any school in the top 25 will equip you well. Want to be an entrepreneur? Any school in the top 25+location of the school matters. Want to get a job at MBB or PE? Go for the M7. I could go on and on, your school selection should really be dependent on what you want to do after the MBA and which companies recruit for which positions where. Fortunately, this information isn't hard to get. Every school has placement reports with a list of recruiters on their website. And any current student should be able to tell you which functions the companies recruit for.
Sorry for being so long-winded, but I hope you take this post in the right spirit.
Yale's MBA is either a great program or a merely decent one, depending on what you're wanting to do. Every program in the top 20 is like that, outside of the HSW troika.
The only ability the GMAT is an indicator of...is the ability to do well on the GMAT.