I don't believe there is any hint in the diaries and letters that indicate that Alexei has stopped his growth and may end up being shorter than Anastasia.
If he had stopped growing, I think this would have been a concern, however, his growth may explained why he had bumped into things in those last months before he became bed ridden. When a child is growing he bumps into things or he reaches for a glass and end up hitting it so it spills.
Because Alexei was bed ridden, perhaps no one even noticed how tall he had gotten since he wasn't standing completely upright up next to any of them.
This last Sat. while at a wedding, as our family was standing and waiting in line to leave the church, I noticed that my grandson, who is 12 has had a spurt of growth. He's grown 5 inches since Aug. and that's only five months.
So, yes, a child can suddenly grow suddenly and quickly.
And, yes, a child may not grow any more at all but that is not tipical for 12, 13 and 14 year olds.
Oh, and let me add, a hemophilia attack does not prevent a child from growing.
AGRBear