Yes, but only if the adapters support VLAN tagging.
That way you would be able to create two tagged VLANs on each adapter, one for public and one for private traffic. You'd also need a switch that supported VLAN tagging, but I think these are fairly common now.
If your NICs do not support tagging then you'd need to get another adapter to allow Sun Cluster to install.
Regards,
Tim