There is countless threads people make here about that, but its a legit concern I guess, we all love piano here, we all dream of it.
In my opinion, it is possible, and the coincidence is that I am 26 too, and I started in the beginning of this year in February. I always had doubts about it before I started, I thought of the old saying "you have to start young to be successful" then I just decided to try it, and my teacher was the first to say, its possible, it may not be very likely but, it's not impossible. In a year time I reached grade 8 or a little higher in practice and I never thought I would progress that far in such short period, so I didn't even know of my own capabilities, and now I'm moving to Canada next year to study at a conservatory. Look at how things developed.. The thing is, if no one done it before, instead of giving up, its better to think you can always be the first! You have nothing to lose, everything is experience and at the end, if you don't make it, you will not regret trying it, and you can always teach, accompany, and also, when we think of "concert pianist" I guess most think of being as famous as lang lang and other tops. There are countless concert pianists in the world, like my teacher, that played in europe, us, canada and japan, and maybe no one heard of, and she also graduated from Curtis.. Moreover, if you start at the age of 3 and go to Juilliard it doesn't mean you will be a concert pianist too.. so this is really two-sided.
Now, evaluating this from another point of view, there are 2 factors that comes to mind. One is how good you are as a pianist, and the second, the piano market. I believe, and I know many teachers who say and can prove by some students they have that everyone dispite age can reach top technical excellence. Some teacher will say no. But I believe, if you have talent, you can play as good as a top. In my opinion if there is one real problem for starting late is the market. I hear many people saying that orchestras look forward to young talents most of the times, so as better as you are as a pianist, the world would choose a younger pianist than you. Also, there is the competitions problem. Many pianists make their names winning competitions. Like, you win the Chopin international competition in Warsaw, well you're probably sure to be a concert pianist the next day. But the competition has an age limit of 30 if I'm not wrong.. and most of the serious competitions, has an age limit around 35.
Just think if this is what YOU wanna do for the rest of your life and if you love piano that much, then and only then you will be able to study and give your best to have the chance.
Hope it helps, it's just my opinion anyway =)
Caio