HBL2350 to control sensorless brushless motors

This is a question regarding the HBL2350 dual channel Brushless motor controller controlling a robot base via 2 robot drive wheels. Can this be set up to control brushless motors that don't have hall effect sensors, specifically the Outrunner propeller motors that seem to be relatively cheap? We were thinking of attaching rotary encoders to the output, or are we better off getting brushless DC motors that have hall effect sensors and using those for our position input.

The HBL2350 only works with motors fitted with hall sensors.
The outrunner motors you describe are a great value and deliver a lot of power for their size, but sensorless motors need to be rotating before a position signal can be sensed. So they will not run well at very slow speed and are therefore not the best choice for robots.
Beware too that they tend to be overrated and that they depend on good airflow (which is generally available from the propeller in an RC aircraft setup) for adequate cooling.
You should find it advantageous in many ways to use a sensored brushless motor.