Short Answer
Yes
Long Answer
Servers belonging to the same account are grouped into the same private VLAN. As such, you may assign any RFC 1918 private address to your interfaces. They will not conflict with any other customer.
Additionally, since the servers belong to the same private VLAN, using private addresses for server-to-server communication is not necessary. In fact, you can communicate between servers using their public IPs and since the traffic will not leave your VLAN, you will not be billed for the traffic.