I'll test it out today. I did have a game recently where I know for a fact the icon stays the same (ranged promotion icon on the knight) but I didn't actually check the combat. Could just be a visual thing.
As for chariots, I think they are great. Unless you are rushing Xbows, there is a gap between CB's and Xbows, in which case they are essentially CB's with much more movement. My main problem with them and why I don't use them as much is 1.) promotions (although will check to confirm) and 2.) while it is never going to cripple you if you have too many CB's/Xbows, having a lot of knights sitting around isn't all that effective. i.e., the role change upon upgrade.
If I do try and use them, I will mix, like I did in the recent India games I've played. A few elephants, a few CB's.