F5 communication with pool members

Hello community,

Is it possible for an F5 to load balance traffic to pool members in a network segment if it doesn't have a self-IP in that network segment?

**Please refer to the diagram attached***

To give you more context, I have a virtual server configured with a DMZ IP(172.16.1.10) and I want it to load balance across servers in my inside/trusted network (10.0.0.22 & 10.0.0.23). If the F5 doesn't have a self-IP in the 10.0.0.0 network, is it able to load balance across the pool members?

If I have a self-IP in a different network, say 10.0.1.1 network and I create a rule in the firewall to allow traffic from that IP to the pool members, is that sufficient?

Thanks.

CC JRahm