No. Only the +1 move from Mongol UA would carry on to cavalry along with any other movement promo u might had chosen for ur Keshlik. Overall cavalry movement will be 4 compared to 5 of Keshlik in normal circumstances.
Side note : Don't upgrade ur Keshliks to cavalry. They are simply too good. They have ranged attack & faster movement. With proper micro they can literally annihilate cavalry & rifles.