The answers are yes and yes.
I always ran three brakes on my bike, the coaster can be a little harsh for certain things - manuals for instance. Only back then they were called coaster wheelies..... or gliders..... and most all backwards stuff I never used the coaster.
As for you second question, why would you want to leave the arm off? Fit it and use it
Remember though if you leave the arm off, you'll still have to 'set' the coaster first. A tiny crank backwards (a couple of inches or so) just as you're settled before the ramp.