Is it possible for the master brake cylinder to be bad even though there is no outward sign of damage or leakage?

Yes, the piston cups can blow out.

X2. Usually can't tell by looking at it. If you're having problems check for leaks everywhere in the lines and at the wheels. If you find none it is most likely the master cylinder.

k, thanks.

X3. When an internal failure has occurred, my experience has been that the pedal will travel to the floor when the pedal is first pressed, and when the pedal is then released and reapplied, there is full pedal.
The other common failure mode is a leaking piston seal where the master cylinder mates to the vacuum booster, and in that case, the brakes will operate normally (unless the fluid level becomes too low) but you'll see brake fluid running down the front of the booster.