^yes - worked in my oldish Egypt campaign (*finished with veni, vidi, vici yay*) half a year ago....and is working exactly like that in my fresh Bactria campaign. (started after the update, so no leftover...cleared old files and such)
I never really paid attention to that in my last campaign (Egypt), as I typically use the women to maintain loyalty/public order and alike ..
I try to get most of my beneficial fighting generals and keep them in my house, but usually one of my 2nd or 3rd in command is from another house - that makes it much easier to maintain the balance. Every other general does province maintenance and provides food/tax/+++ income + PO and I can upgrade them just fine, even if they haven't seen a single battle.
(and I hammer that promotion-button as soon as it is available *cough* - less upkeep/ more mA/MD ^^ more public order .. more of everything)
That being said, in older DeI versions, the promotion was capped at a certain point and only battle could get you further promotion. But that's quite some time ago....and more or less experimentental for only Roma at the beginning. With the general update to Emperor Edition a few things were added from CA...and DeI adapted to it and changed accordingly.
While I barely finish my campaigns..it's safe to say I watch the DeI evolution nearly since the beginning .. closely
I wanna have that BaI in all my TW games...but KAM got lazy lately. (I could take over at least the warhammer proper_combat)
edit: no offense, KAM :> I know you are involved in a crapton of other things...