Yes. You can train a unit in an under developed province, retrain it in an armour province for the armour bonus, retrain in a weapons province and retrain in a valor province. It takes a lot of extra moving, so many people just build the armour in the valor province and have a separate weapons training province. If you need to fight in the desert it makes sense to have a separate armour training province so that you don't train your desert troops there, just your others.

mfberg
(rambling thoughts about any subject, no coherency is implied or intended)