Does a Car Battery with a dead cell cause failures of alternators?

This is no doubt a superior test method but typically, a home mechanic will not have this equipment nor the inclination to bring it to a battery store to pay for having it done. I use an informal (quick and dirty) test if there is doubt about the battery. Turn the headlights on and start the engine and immediately shut it down before the alternator recharges the battery. If you can do this 10 times in cold weather, your battery should be good for a while. Not very scientific and the alligators might snap their jaws about deep cycling a battery but it has worked for me.

Before multiple coil electronic ignition, I would ground the ignition coil output and let the starter crank the engine for 30 seconds if it would.