Will the engine rev with or without the.....
 

Will the 3rd gen or any other rx7 engine rev smoothly or above 2500-3000 RPMs. with the alternator remove or not intall?

Removal of the alternator should not affect engine the engines' smoothness. You have a electric water pump right?

I am just trying to hook back up everything on my 3rd from doing a single turbo mod and the engine is not reving properly to full power. I must have missed something but I will like to know if the engine will run and operate normally wiht out hooking up the alternater.

It may run too rich at high rpms and possibly backfire without the alternator.

I stomped a VR-4 on the way to the auto part store with out the alt hooked up.

Is this with an aftermartket fuel computer or a stock car?