Yes! A battery that has a bad cell runs at a voltage considerably lower than the normal 13V - 14V with the engine running and the alternator charging. Lots of modern alternators do not use permanent magnets, but a field coil to provide magnetism to the alternator. That field coil (an electromagnet) takes voltage from the battery to create ...

This to me sounds like either a bad front orifice tube (or thermal expansion valve depending on the system) or a blockage in the front part of the system

What does it do, does the engine turn over at all?

Usually, to adjust the brakes with those ''star wheel adjusters'' (assuming they work properly), you put the truck in reverse, pick up some speed, and make a harder than normal foot brake application. If you do this a couple of times and your adjusters work, this should tighten up your rear drum brakes.

Supposing you're talking about a car with an automatic transmission, nothing really... It just won't start again before you put it in neutral or park. Same thing for a manual by that matter. Worst thing that can happen is if you're not parked on level ground ;) the car might move