I believe armour stats gained through armourers have exactly the same effect as being armoured in the unit description (if you see what I mean). So up-armouring a unit does affact its performance in the desert just as it would if it was armoured to start with. Up armouring an already armoured unit gets a double effect. I thought JHI were heavily armoured though.

Personally, if I can I leave a province or two without armour upgrades to create troops for the desert, and obviously I try not to take troops who start off with heavy armour anyway. Its nice to have a "proper" desert army but its not especially worth worrying about to the Nth degree, there just aren't enough desert battles to be worth a major bother.