Should your car run correctly with no alternator connected?

I am having an electrical issue that is driving me NUTS and if someone knows the answer to this it would be appreciated.

 

Are you just not sure if it's your alternator that's causing the problem? It will drive ok, but it will get worse and worse over a very short period of time, as you're just running the car on what power the battery has left (since the alternator isn't charging it).

 

ok but with a fully charged battery it should run completely normal?

I am sure my alternator is gone and have tried a used one I had that I thought worked but there was no change. I took it to get tested and it was bad as well, so I am thinking I have something that is causing my alternators to go bad. Very odd, right out of the blue

I am getting bouncing voltages across the battery, even with no alternator.
As well the multimeter goes crazy if I have the leads near the engine bay which makes me think I have a short to ground somewhere but cant find it

 

I think it should run ok with a charged battery, but probably not 100% perfect.

Is your negative grounded properly? Check all of your negative cable's ground points from the battery terminal to the fuse box. I have a DA, so my negative cable runs from the fuse box in my engine bay, to my battery, I believe they are also linked to another ground cable under the battery box that runs to the tranny.

 

I dont think it is my grounds because I checked them all.

I cant figure out why my voltage bounces, measured across the battery with no alternator, Im guessing this has something to do with it running rough

I want to fix what is wrong before i put another alternator in and risk damaging it

 

I started thinking my ELD was gone so checked the underside of the fuse box and there was no ELD connector.
Is this normal for a 98 Integra?
Does that mean it isnt the fuse box that can be giving me troubles?

 

Your car will run with a fully charged battery until it runs out. Take the alternator Checker/ Schucks/ Kragen and have them test it.

 

there is no alternator on now, the alternator is gone but the car still isnt running right with full battery and I suspect there is something else wrong that caused the alternator to go.

So I am trying to figure it out before i risk blowing an alternator