I don't mean concert level virtuoso but enough to be able to play some of the basic repertory, mostly for personal amusement.
BTW, I'm 29, and i have never touched a piano before. 
I do believe it's possible
There's a good book that I don't remember the author of called "The Myth of the First Years"
As you probably know it has been said that the first years of life are somewhere fundamental to learning and what you can achieve in those years you will never be able to achieve later. According to many researchers and experts this is a myth nowadays caused by a biased belief in nature where it's actually a matter of nurture
For example it has been found that a person of whatever age has all the physioneurological conditions to learn a second language and speak it as a native (it has happened before)
So why everyone think it's so hard?
The reason is one of cultural fruition
It has been observed that a child is more spontaneous in creating bonds, in talking with foreign kids and making friends. A older kids will try to spend most time outside where he can listen people talk and communicate.
Adults on the other hand tend to eschew from creating bonds so easily, try to find people that speak their native language and spend more time with them than with the foreign people and also have less time ... most of their time is spent at work where usually communication is mono-chord and rather repetitive
Another reason is neuromuscular
We produce sound by reasoning the vibration in the mask (lips and tongue)
Since muscles have memory the more time we spend moving the lips and tongue in a way functional to the sounds we have to produce the more spontaneous will be to use the same movements when speaking anothing language, while the condition to make the exact same sounds it to "recondition" the muscles
In other word while a child have still not muscle conditioned to its native language a teen or adult must do the conscious effort to recondition its muscles
Apply that to the piano and you'll say why it's wrongly believe that you must be start as a child in order to master the virtuoso technique at the piano
1) a child has more free time and less cultural barriers
2) a child has muscles that are less conditioned by a long time of repetitive tasks at work or school or in sport
3) a child is more spontaneous and see the piano for what it is, adults are more entrapped into cultural symbolism and tend to not see thnigs for what they are hence it's harder for them to grasp concepts on their whole
The solution is to "make a child out of yourself"
Hence reconditioning your body and mind to be free from "conditioning" like that of a child. The free from conditioning mind and body can in turn be easily reconditioned to the virtuoso piano playing
In other words you have to make a conscious effort to reprogram your muscular neurology knowing that it has been conditioned for a longer time compared to that of a child and reprogram your analytic versus analogic mindset knowing that it has been conditioned for longer compared to those of a child