HDCP is the protocol that is used for encrypting the signal going from the source to the sink/destination. If the monitor supports HDCP "over" DVI, it means that it has a chip inside it (most likely from Silicon Image or Broadcom) that can handle HDCP. The source device will have a similar transmitter chip for HDCP over HDMI (or DVI). These chips are specific for HDMI or DVI - "but" the HDCP protocol that is running is the same.
That being said, you shouldn't have any issues. I've seen HDMI to DVI setups working with a HDMI-DVI adapter wrt HDCP. If there isn't something severely wrong with your h/w, it should work.