Since you have to ARP in order to get anywhere, the first hop is by necessity to the default gateway. The first L2 destination must be to a core switch. After the L3 translation, the packet goes to the final L2 destination.
If the core switches had the intelligence to reply with the final destination's MAC address on the ARP, then it could work like you describe. It would be a dangerous thing to do, though. It would break the protocol somewhat.
To know whether things work like they should, sniff for the ARP reply at the originator to find out if the core switch uses warped intelligence to subvert L3 protocol and make things go that little bit faster. Actually, just look for the destination MAC address on any packet - it will tell the truth. |