Sure. The old MC was indeed bad, and most likely did allow air into the system, but if you don't bench bleed a master cylinder before installing it, it will pump a boatload of air into the braking system. Air rises. If you have pedal pressure and there's air in the system, those air bubbles will rise back up the lines into the proportioning valve and the MC, making the pedal pressure inconsistent. The diameter of the MC is different than the brake lines so the amount of air in either one will make the pedal pressure different. Air compresses, brake fluid does not. If you're mashing the pedal and you can't lock up the brakes, 99% of the time there is air in the lines.

You don't need to bleed your brakes once or twice. You need to bleed them until ALL of the air is out of the lines, and you need to do each wheel cylinder in the right order or you won't get it all out. TOY4TWO posted that order, and can attest to how much of a PITA it is without bench bleeding. It's a lot more work, sure... but if you're going to do this kind of work yourself, you HAVE to do it right and get all the air out or you're putting yourself and other people in danger.

At this point, you're better off not removing it and bench bleeding it because there's already a ton of air in the lines. You're going to have to bleed that out anyways, so pick up an extra bottle of brake fluid, start bleeding, and don't let that reservoir run dry.