And indeed its the same on the Airbus, the Rad Alt height is displayed on the PFD <2500ft, but the system kicks in well before that.
Don't pin me down on the exact height, but I believe it is somewhere in the order of 5000ft.
One of the things you can notice this by is the fact that if you press the approach pushbutton to arm the Loc / GS above 5000ft, you will only get CAT 1 displayed, when descending through 5000ft the rad alt kicks in and you get CAT 3 Dual, if you're fully serviceable that is.