Sadly no I don't believe players grow in height. And I've found a method that tends to be less focused on each individual player and more focused on something more in your control which is the ability of your training staff as in who you hire on your staff because coaches tend to be very cheep...
I don't know if this is a bug or not but I'm in the 2042 season and I want to add another coach and the game just won't let me. The menu for adding another coach is just blank