Should I be able to hear VTEC-E kick in like normal VTEC does?

 

With a stock airbox and exhaust, not really.

 

VTEC-E is on the intake side only....and it's only 4 of the 8 valves that start opening bigger (and then they simply match the other 4 standard valves). It's not going to make a very noticeable sound. Even still, If you ditch the resonator box and tube down inside the bumper (provided you still have them), you would have a much better chance of hearing something.