No, the AI heads straight for your hidden units.
This I have not seen much Now of course the AI has to know where all of your units are, hidden or not, or the game would be unplayable, but I love my traps and 99 times out of 100 I get to spring them without the AI "cheating" by heading straight for my concealed units.

Roman Cav loses to Greek Cav
Are you referring to Equites or the post-Marian 'Roman Cavalry'? Agreed that Greek Cavalry is not all that great, which is why as the Greek Cities I hire as many Sarmatian Heavy Cav as I can. As Macedonia you get lots of nice cavalry so no need for mercs.

On M/M I am already seeing a difference in my losses
Which is going to force you to change your tactics a bit, and it makes having good (5-star+) generals leading your armies. Don't neglect even the slightest edge you can gain from inherent general bonuses or those from ancillaries. All those bonuses stack and become unit modifiers to your troops. That's why I stated earlier that when you get your "Military Genius" (usually comes in the second generation), don't ever let him see the inside of a city. When I play Armenia, that general will lead nothing but a Cataphract army...all Cats and Arab Cavalry, and not ever a single infantry unit. Of course that's just my preference, but it pays off when he reaches legendary status as a horseman, attacker, defender, and/or conqueror.