The politically correct version would be "no, age does not matter at all! As admissions officers, we treat everyone equally and base our decision purely on merit." Which is pure BS.
I wrote an article/blog about this a while back that goes into detail why b-schools are going younger:
https://www.mbaapply.com/advice2.htm#age
The Cliff Notes version of it is this:
(1) Going after those who normally would do law school or med school; unlike years' past where most kids went straight into JD or MD programs from college, most of the incoming JDs/MDs aren't fresh college grads, but are 2-3 years removed (i.e. 24-26), and most would've had some work experience. B-schools want to compete for these kids.
(2) Women. Biological clock -- getting women to go back to b-school in their late 20s is a tough sell, and b-schools will lose out on many strong candidates. Makes more sense financially if you can work a few years post-MBA before having your first child (again not every woman thinks like this, but there's enough highly accomplished women professionals that do). That means going to school mid-20s, so you have the option of reaping some post-MBA income and still be able to have the option for kids in your early 30s. And unlike law or med school which has been 50/50 male/female for a while, b-school is still majority men. What they can't solve is that MBA women are overwhelmingly American (of any race) or Chinese (China, Taiwan, HK, Singapore, etc.). In the rest of the world, the business/corporate world is still a man's world.
(3) US underrepresented minorities (black, hispanic, native american). Within these subcultures in America, minority families with overachieving kids tended to view law or med school as the primary means for social/econ mobility. Perception was that corporate world was heavily stacked in the white man's favor - and why do a fancy MBA so you can run a family biz like your Uncle Ricardo who is doing just fine but with an associates degree? Even amongst Asians - it's still med school, and everything else is a distant second. So this intersects with (1) above - target more folks who otherwise would've done MDs or JDs, and you likely get more minorities to apply.
(4) MBA recruiters want young meat. Let's face it. No matter the ups and downs of the economy, mgmt consulting and finance still take up the lion's share of MBA recruiting, even at HBS. These industries are churn and burn. Their biz model is based on partners selling services that cheap labor (i.e. young MBA grads) execute. They get old, they get expensive, they want time with kids, they want a "life". Easier to chain a 26 year old single guy/gal to a desk or have him/her live in an airports and hotels, than a 30 year old married guy/gal with spouse and kids. Even tech companies like Facebook, Google, etc. like them young. They make their "corporate campuses" so cool and comfy because they don't want you to leave. Or have a life, because why have one if we provide everything for you in our offices? We can even help you "relax" with massages, spa treatment, lots of video games, toys, etc. Young people fall for this shit. Older folks know better and see through it - or they actually have a spouse and kids to go home to.
(5) Product differentiation. If the folks in a full-time program look more like the folks in the exec program, why bother paying more than double the fees for an exec program?
So yes, it is a disadvantage. For some schools it's fatal (HBS/Stanford), for others it's a disadvantage.
Of course, I'm sure there's going to be folks that pop up and say "well, I'm 36 and doing a full-time MBA..." but for every one of them there's a larger percentage who are older who didn't get in.
This "age-ism" understandably gets some of the older applicants and students riled up, but it's one of those things that has to be brought out in the open. Yes, you can certainly get in as an older candidate, but you also have to know that it's an uphill climb and adcoms do care about age, no matter what they say publicly.