When completing my application I had a lot of trouble with this. I trimmed mine down to less than 2000 characters WITH spaces, and it still wouldn't let me submit the item.
It will not let you submit it if it is over the 2000 limit, but is SEEMED as if it were counting spaces as characters.
I know this isn't a clear yes/no answer, but I hope it helps.
Also, I met with the Director of Admissions, and she said trim it til it accepts it.
J.