Yes, Predator can send/receive programs to/from your Dyna. If you've matched the DNC Properties in Predator (Baud Rate, Parity, Flow Control, Data Bits and Stop Bits), you should be OK. Your cable needs to be wired correctly.
What happens when you send from the Dyna to the PC? Get Predator ready to receive first, then send from the Dyna. Anything?