I'm an electronics newbie.
The part I'm talking about is this:
DC 10-50v 12V 24V 48V 3000W 60A amps DC Motor Speed Control PWM HHO Controller
My question is, can this type of part be used to control brushless DC motors?
Practically all brushless motors require 3 independent power connections, each one at the appropriate frequency and 3 different phases. Those 3 power cables are typically connected to a brushless ESC.
Practically all DC motor speed controllers (including DC electronic speed controllers for brushed DC motors), including the one you link to, only have 2 output power connections.
The 2 outputs of a DC motor speed controller are not enough to drive the 3 inputs of a brushless motor
(photo from "RC Hobby Mysteries: What is Brushless Motor?")
(diagram from "Esky Helicopters FAQ: Brushed vs Brushless Motors")
DC motor speed controllers -- with 2 output power connections -- work with brushed DC motors that have 2 power connections.
Brushless ESCs -- with 3 output power connections -- work with brushless motors that have 3 power connections.
As far as I can tell, any other connection between any two of a DC motor speed controller, a brushless ESC, a brushed DC motor, and a brushless motor, won't do anything useful.