it works at the kernel level. I added 240.0.0.1/4 to my ethernet device and it tries to ping (but finds nothing, because there is no other device on that network to respond). I can ping 240.0.0.1 since it's local. This is all on a desktop linux machine running Debian and kernel 4.16.0 and adding the addresses as "ip addr add 240.0.0.1/4 dev eno1" and "ping 240.0.0.2" (arp doesn't work because this device doesn't exist) or "ping 240.0.0.1" (works fine, since it's a local address) i'm using "iputils-ping" for pinging.
EDIT: Behavior is the same when I log into an OpenWRT router and manually add a 240.0.0.1/4 address using ip. I am not willing to reconfigure my in-use access points etc. and I don't have a test device to test it on, but if @lleachii is seeing some other behavior it's probably due to some UCI config checking and refusing that address range rather than a fundamental problem in the kernel or other binaries.