Eclipse is connected to my rooted phone and I can run debug sessions and see LogCat messages. I can also see the phone in Devices view in the DDMS
Devices
DDMS
File explorer in DDMS works fine with real devices. Just use the stand alone one, not the Eclipse plugin.
From the command line, type ddms.bat, then select the (real) device, and only then select Device > File Explorer from the menu:
ddms.bat