There is no feedback to the lm338 to alow it to atempt to hold the plating voltage within 30 mv. so it can not do that. The constant current source is designed to hold the voltage across R12 constant thus holding the current constant through the plating tank. The impedance of the tank controls the voltage across the tank.
all the 338 circuit does is remove most of the ripple on the input supply and thus improve the current regulation. It also shares the power dissapation with the mje3055.
The IRF540 is just a low value resistor as configured. The unconnected lead would allow on/off control by a remote device such as a timer. The transistor filter in the control leg of the 338 is of dubious value given that the currnt source will drive the tank voltage.

It will do what you want but has some interesting issues. There are other simpler designs that would provide closer control (this lacks solution temperature feedback for example)
By its design it is an inefficient circuit as it dissapates most of its power across the regulators rather than the load. Terry