I'm sure Conner as well as all MMA fighters train with heavier gloves. I did
When you step in the ring the idea is you trained with heavier gloves, and putting on the lighter gloves leads to faster hands and more stamina.
I remember the first time I stepped in the ring when I was younger I thought they handed me the wrong gloves lol. My hands felt so quick because I was used to training with 20+ oz gloves.
That all being said while I respect McGregor as a great MMA fighter I would be shocked if he puts up a fight against one of the all time great boxers. Floyd should be able to work McGregor all over the ring.