@george1421 Thank you for your help. I managed to speak with one of the techs from our central IT this morning. He informed me that they block PXE boot on our network. PXE traffic is automatically being filtered and dropped by the switches. I think it is unlikely that they would add my FOG server to the DHCP relay. Which makes sense I was only able to get tcpdump to see the discover traffic when I connected both machines to their own unmanaged switch.
Still not sure why dnsmasq did not respond to the DISCOVER packet. I will try reinstalling the service. Although following this revelation I may just reconfigure FOG to run DHCP and use it on its own isolated network. Thank you!