The Australian ship Ocean Shield has detected multiple pings from the black boxes onboard the missing Malaysia Airline Flight 370, specifically on 4 lines of bearing according to this article. The same article also states that they need a few more lines of bearing in order to further narrow down the search area.
So my question is pretty much as in the title - can they use doppler shift to help figure out where the pings are coming from? IIRC, they used the doppler shift from the satellite data to figure out that the aircraft was most likely on the southern of the two arcs that were proposed several weeks ago.