Skyyr,
The original situation was a zoom up and dive down, not a stick-to-the-belly immelman turn. It is true that in the initial phase, to get the nose up you have to increase AoA and pay with a little induced drag. I say "little" because normally you start from high speed and induced drag goes down with speed:
(Image removed from quote.)
"L" the lift is proportional to "G" for a given mass, so you can treat it as G. Yes, the drag goes up strongly with G, but it also goes down with the square of the speed. At the typical 300 mph speeds of the pony, parasitic drag is still a significant part of the drag as long as you do not pull more than 3-4 G (so G^2 factor does not go wild). This will take you about 6 seconds to point the plane from level to 70-90 degrees up. However, the moment you started to lose speed, you also reduce the parasitic drag which is a very significant part of your drag at those speeds. The net drag *almost* always goes down and shifts the energy balance to a net positive. You spend long seconds at speeds in the vicinity of 100-200 mph (up and down) where the parasitic drag is low, prop pulls well and induced drag is nearly zero because you are zooming. This is where you build the energy. By the time you stall at the top of the zoom, you have more energy than you started with - unless you were totally hamfisted with the stick.
Easy exercise:
go offline, fly at 0 feet above the water at 300 mph and pull into a vertical zoom. You can watch the G meter in the cockpit. Do your hammerhead/whatever at the top, come straight down and pull at wave-top level. What's you speed now?
A flat turn is generally inefficient energy-wise because you are using part of your lift to maintain level flight (and pay the induced drag), and keep the high-speed high parasitic drag component throughout the maneuver. This generally leaves very little room for net energy gains.
Regarding drag, yes, parasite drag is a source of drag, but it's a not a functional problem in maneuvering because it's most significant at cruise speeds, where the airspeed is of the least concern to the pilot (if you're fast enough for parasite drag to be significant, you're fast enough that your energy state is not a problem). Slowing down to the point that it's minimized is unreasonable in the scope of energy conservation, as it requires the pilot to maintain a speed that makes vertical maneuvering impractical (corner speed). In other words, the only time it matters on paper is when it doesn't matter in flight, because your airspeed would be increasing significantly. The average WWII-sized aircraft aircraft has a parasite drag profile smaller than the size of dinner plate. This can't be changed, so therefore it's not something we actually consider in a combat environment (or a flight environment, for that matter), outside of Va and Vne speeds (and flap/gear extension speeds, but I digress).
Induced drag, however, varies directly with the load put on the aircraft, which is why it matters in the scope of energy conservation. Pilot input does affect it through every phase of flight, whether slow or fast, low or high.
Regarding the Immelman, you're confusing the acceleration given by the aircraft's engine with energy conservation of the maneuver. Try what's described above in an aerobatic glider and look at your airspeed after performing a climb, hammerhead, and extension back to the deck - you will show a loss in overall speed. I know, I've done it more times than I can count.
Further, even straight vertical, you will have induced drag unless you completely unload the aircraft to a 0G configuration, which is impossible to fully do in a WWII aircraft and still maintain straight vertical orientation. Even when vertical, you will have a 1G load on the wings. It's not that much of a load nor is the induced drag significant, but it's not the pure energy gain you're implying it to be.
I'm not arguing that you won't accelerate in a dive with a running engine; this thread is diverging away from the original discussion, to which my original point was that any time you maneuver, energy is lost, including when maneuvering to the vertical. The scenario of diving back down or extending to gain back from the engine is not part of the maneuver, as the Immelman ends the second that you roll wings level after coming out of the top of the half-loop. If you killed your engine and dove back to your starting altitude with a wings-level orientation after performing the maneuver, you'd find that you would have lost airspeed. Just because you are in
a better position to regain energy doesn't mean that you actually
gained energy - this is one of the fundamental concepts in more advanced energy-fighting tactics.