My guess is "no".
I connected a Cisco router to a switch and SPANed the port. I didn't see any IGMP membership reports for 224.0.0.1 or for 224.0.0.2.
On a related note, how do Cisco switches handle multicast for 224.0.0.0/24 any differently than for other multicast ranges if hosts do not send IGMP membership reports for 224.0.0.0/24? If they don't send IGMP membership reports for that range, my best guess is that a Cisco switch would flood all traffic destinted for 224.0.0.0/24 across all ports in the same VLAN on the switch (and any trunks that do not have that VLAN pruned).