What they said.
As for access, another popular method for servicing the cluster is to remove the driver's side air vent from the cowl under the hood. Once that's out, you can easily get to the back of the cluster as it's right there.
But if you're still young and flexible, you can do it on your back. Personally though, I only like to do that when I remove the driver's seat, so likely I'd just take the whole cluster out and let it sit there hanging under the dash or sitting on some sort of support stand while you work.
Heck, you could probably just leave the ammeter hanging off the wire if you needed to. But since that plug is there for this very reason, go ahead and use it. It's a good idea to pull it apart when working under there anyway, to inspect it for rust or any other problems.
And take what Steve said to heart. That Black w/yellow wire IS your main feed that everything else takes power from. That's your "charge loop" if you will, where one end is (or used to be in your case) on the back of the old alternator and the other end is at the starter relay. It's how everything is powered and how the battery is charged.
So yeah, it's pretty important to leave it intact or splice it permanently like Steve suggested. As said though, if the connector looks to be in good shape, just keep it as is and make sure it's plugged back together nice and tight.
Since it's only powering your cabin accessories now, and no longer has battery charging duties, it's load is reduced. This is assuming you now have the larger 6 or 4 gauge cable from the alternator to the battery?
As for powering the new volt-meter, don't bother with the big Black wire. Simply take the power for the gauge from the input side of the IVR, or from the stud on the back of the ignition switch. Both are very convenient to the gauge, with the IVR literally being there to power gauges already, and only with the key in RUN.
Just don't use the normal output side to the gauges. Use the input side from the ignition switch.
Paul