Yup, the 6.2L has a mechanical lift pump, and the injection pump is capable of drawing it's own fuel if required (runs poorly and smokes a bunch though). However, on the IP itself is an electric fuel cut off solenoid that turns on and off with your ignition switch. That is what allows you to shut the engine down.
If you are putting a new alternator in, install a CS130. They are a 105 amp alternator vs the 63amp you've got now, and are very common.They are found in just about every vehicle GM made from 87 or so up. There are two versions of the CS130, one will fit your truck, the other won't without fabricating new alternator brackets. The CS10 you need has the mounting ears 180 degrees apart from eachother, the other has them some other angle apart. You'll find it in certain cars at the wreckers, not in any trucks.
Installing it is easy -- The alternator bolts straight on. TheBig red wire on the post like the old one, pink / black wire runs to keyed ignition, brown wire either goes to your idiot light in the dash (if so equipped) or to a 12V power supply through a 75 ohm, 3 watt power resistor (or a 194 / 168 marker light bulb, which is effectively the same thing). Take the V-belt pully off the original alternator and swap it on to the new one.
GM makes a plug that allows you to convert to the CS130 alternator without doing any wiring. There is one that has the resistor built into it for vehicles without the idiot light, and one that is a direct connection for those that do. It costs around 30 bucks or so, and can be found at almost any GM dealership.