I'm replying because no one seems to be answering your question!
If you plant a seed in the ground, how long will it take for a tree to grow?
OK, it's not really an answer. So here is the answer.
It depends of the type of soil, the weather, sunlight, if there is a larger tree blocking, the pests, the fungi, etc. But you probably knew all that.
A better gauge -- having read the posts of some of the teachers in this forum, here are some estimates. I assume that one is able to start on Chopin’s etudes if they are able to finish their grade 8 ABRSM. (There are 8 grades in all, after which you start your diploma.)
The fastest claim I've heard is that anyone who learns to play the piano in the correct way can get up to about grade 5 in about 6 months to 1 year, and grade 8 in about 2 years. I have no reason not to believe this claim. Let say then that it is possible to learn your first Chopin etude (without struggling too much) in 2-3 years.
However, the ABRSM board expects that a student takes one year for each grade (there are 8 ) and in addition one or two extra preparatory years. In which case, you would start learning it after about 9-10 years. This is supposedly the average.
The upper bound is of course infinite -- you never learn a Chopin etude, which applies to the majority of people. In fact, probably even the majority of people who have learnt to play the piano at some point in their lives.
al.