Yes but DHCP packets are only sent rather infequently. My understanding of it is that DHCP will attempt to renew at 1/2 the lease time, and again at 3/4 lease time.

So if your DHCP lease time is set for 1 hour, you should expect to see DHCP magic packets roughly ever 1/2 hour ( assuming your DHCP server is working ). If the DHCP server was down, you would see some packets at 1/2 hour, 3/4 hour and finally at 1 hour. Then it gives up.

It sounds like he is seeing quite a bit more traffic than that.