It can be but you will need a relay with the capacity to carry at least 40 amps (based on your diagram, your brakes may require more).
I would suggest a relay similar to what is pictured below. I wouldn't go with anything smaller than a 50 amp continuous duty.
Continuous Duty Solenoid 80AMP 12V
You could also use a relay like the one below, but I haven't had good luck with this style when used for high amperage.
12 Volt DC 50 Amp Continuous duty
I would connect the contact circuit directly to the fuse that's connected directly to the battery, with the other end connected to the brake controler. The control circuit can be connected to almost any key on power source, as it only draws a small amount of current