Based upon the 300 ohm impedance of the HD650 and the output voltage at high gain of the DX50, it would appear that only about 10ma of current can be delivered to the phones so unless you are content to listen at fairly low volume levels, it is unlikely that the DX50 will provide adequate sound levels without an external amp.
To expand on your math:
3.1V / 300ohms = 0.0103333 amperes, or 10.333ma of current (like you said)
but since power (which is what we are concerned with) is calculated in watts = volts * amperes
watts = 3.1V * 0.0103333 = 0.0320...watts, which equals approximately 32mW into 300ohms
32mW into 300ohms is not bad at all, better than a lot of portable amps, and I'd say enough for the 650s