Beagle bone black PRU program using DDR3 RAM
Yes.

The Technical Reference manual for the processor says that the PRU has "access to pins, events and all SoC resources" which suggests it can read and write to DDR3. Further on it in section 4.3.1.2 it discusses the local data memory map and states "The PRU accesses the external Host memory map through the Interface/OCP Master port (System OCP_HP0/1) starting at address 0x0008_0000". Which confirms it.