Smiths, Exp Temples and Weapon temples

[Melea Lord]

Can smiths upgrade troops that can't be recruited in the city it's in?

Same for exp temples?

And for those temples that upgrade your armour and weapons?

You see I can upgrade my screeching women (made in shrine to freyga) to have a silver weapon and silver armour but only have 2 exp (I think the shrine of Donar does this) (I have edited the temples). Another german temple upgrades troops to 3rd exp (Shrine to woden) yet this don't work on "religious units" that it can't recruit. Shrine to Abnoba also works on other units.

So my smith works on oither units, my weapon temple works on other units but my exp shrine doesn't work on oither units. Is this true?