The HH506RA uses a thermocouple as a sensor. It can use multiple type of thermocouples. A thermocouple puts out a voltage, that varies with temperature. The voltage is created because two dissimilar metals are welded together at the tip of the thermocouple. The dissimilar metals actually create a very small voltage, and the HH506RA reads this voltage, and knowing the type of thermocouple, turns that into a temperature.
The sensor that most motherboards, and many of the bay type controllers use, is a thermistor. A thermistor is a resistor, that changes in resistance with respect to the temperature it is at. To measure the change in resistance a small current must be run through the thermistor, and then the voltage is read.
THe HH506RA does not have the circuitry to inject a current through a thermistor, so it is not possible to create a connector to convert a thermistor to a thermocouple. It could be done with an active circuit, but I have not seen anything like that available for sale. I could design one, but in the end I'd need to charge you more than just buying the right controller and sensor.
FYI, my experience is that the thermistor on most motherboards is 10K nominal at 25C, and designed for a R25/50 Beta of 3435K. So when buying a thermistor you'll need one with those specs to work with most motherboards.
Sorry the answer is No... but at least you won't have to bang your head against the wall any longer wondering.