Hello Alison,
no you cannot use RFC 1918 unicast addresses in place of multicast addresses
However, within multicast address space 224.0.0.0/4 there is a concept equivalent to private addresses and they are the scoped multicast addresses 239.0.0.0 239.255.255.255.
Multicast addresses are not assigned to router interfaces and cannot appear as source addresses in IP packets, rather a multicast address represents a session (like a TV channel).
Router interfaces on the contrary can use private unicast addresses taken from RFC 1918 with no problem and you can carry multicast streams over your network regardless of what type of unicast addresses you are using on your links.
You may be interested in carrying only some multicast groups over the new radio link and not all possible multicast groups, are you?
Hope to help
Giuseppe
