Yes. I try never to have to bleed more than the particular brake component I have removed, because of the frequent threads on bleeding difficulties.
Put a clamp on the rubber hose, or if you don't like doing that, prepare a tapered wooden plug, undo the hose, and quickly ram the plug into the end before any fluid has run out.
I think left and right calipers may appear interchangeable, but the bleed nipple has to be uppermost. If you get the wrong one and have the nipple at the bottom, it can't bleed properly.
Fill the chambers with fluid with a syringe on the bench, plug the holes, fit the caliper and pads, quickly connect up the pipes. If you are lucky there may be hardly any air to bleed out.
Don't press the pedal right down in one go - do it gradually letting it return each time. You don't want the master cylinder seals travelling over a possibly corroded section at the bottom of the bore.
A warning about levering the pads/pistons right in. This sends old dirty fluid back up to the master cylinder, which is a notorious way of spoiling its seals and creating a new problem. You are supposed to release the excess fluid at the nipple. Of course if you are replacing the whole caliper that won't apply.