Short answer "no" ...

Longer answer.  

You can use the UDR56K-4 in a few configurations to get on the D-STAR network.

There will be an application that turns the UDR56K-4 into a 70cm D-STAR radio that you can use to talk D-STAR on simplex or through repeaters and half-duplex gateways (hotspots).

There is an application in the G4KLX suite that will need to be adapted to use the AMBE daughter card, but allows you to appear as a user on a virtual repeater talking into the D-STAR network.  (This application already works on the UDR56K-4 using a DVDongle for the AMBE chip).

If you have a D-STAR radio, the UDR56K-4 can act as a half-duplex gateway into the D-STAR network.  A workbench version using an external radio and modem has been running for a couple of months, but will become an application to use the UDR56K-4 built-in radio and modem.

There is no application that puts an analog HT on D-STAR.   Fundamental to D-STAR's digital voice is the need for an AMBE  vocoder to be in the path.  This is contained in the D-STAR HTs and Mobiles from Icom.  The conversion of audio to digital and back happens in this chip.  What goes over the air is the digital signal.  It is possible to adapt some analog FM radios with external hardware and software to use D-STAR DV.  There is also a provision in the protocol to have a special hybrid device at a D-STAR gateway to provide the AMBE encode/decode and interact with analog radios, but it has not been implemented.  I could sketch out how that might be accomplished with a second analog radio and a UDR56K-4, but will leave that for another time.

BTW, I was introduced to Zydeco only about 20 years ago. Love it, and occasionally run across a station on my Internet radio, hoo-wee!!!

---