It absolutely should. This would put all the links in the chain made KR capable, as indicated by the "-k" part of the product name.    Just in case I misunderstood the nature of the question, I also looked at the part number specifically. It does show as validated for the M610, so you shouldn't have any sort of compatibility issues there, either.
I have a M100e Chassis, with two M8024-K switches in slots A1 and B1.  I have 16x Poweredge M610s with the Broadcom M57711 cards in them.  I have connectivity across all of the switches  but the Broadcom cards are not linking up at 10gig.  They all show 1000meg in ESXI v6.7..  I need the 10gig for iSCSI, any options here? Troubleshooting abilities please let me know.      
m1000e - M8024-K - Broadcomm BCM57711 - No 10gig