Quite the opposite. Infact, the less E you have, the more important it becomes to manage what you have left in order to covert that into "angles," position, and the kill shot. Think of it this way, without managing your E carefully, you won't have enough power to pull over the top on a rolling scissors and you'll end up stalled or floating right into your opponents gun sights. Or, you may not be able to cut inside your opponents turn, or make him (or her) overshoot. As you can see, the possibilities are almost endless...
I totally get where you're coming from and don't necessarily disagree with you. But, that is not what I meant really. What I mean is the less relative E you have compared to your opponent, the more you are angles fighting, the more you angles fight, the more the fight will devolve into stallfighting eventually, it's the nature of air combat. During this process as relative E states erode, your options (and his) to use E to create angles diminish gradually to the point where it's almost non-existant. That is not to say you don't have to think about E management at all by any means, you will just have fewer and fewer ways available to have effective E management make a substantial impact on the angle or your position relative to the foe, especially since you started out Co-E/Co-Alt and can each theoretically neutralize or counter any move by virtue of E/Option parity..
It is to say that E management becomes much less a process unto itself, for its own sake, to create angles and more simply a secondary consideration while attempting to get an advantageous angle and keep it relative to your opponent. This is especially true the closer the fight gets toward a stallfight. There is a critical point of no return where the angle you have right before you both become E bankrupt and begin stallfighting that your relative angular position will be almost "cast in stone". From that point forward neither of you will have the relative E to change it much, if it all. This is the "riding the edge" phase. Generally, whoever rides the edge of the stall best will be able to change the angle enough for a shot and win, this involves almost no E management whatsoever as you don't have any E to manage. So, from the beginning to that point, E management, as a means to its own end, becomes less and less important than the angles and your position relative the your opponent in a progressive way..