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Try answering
If I understand your question - technically both pumps pull fuel from the tank to the engine, it's just due to the location of the auxiliary electric fuel pump being up in the wing downstream of the header tank (and upstream from the selector valve), it is taking cooler fuel from the lines and pushes any air out near the engine that may be caused by vapor lock/higher temperature near the engine. At the same time, it serves the purpose you mention, that if the aux tank goes dry, and you select the main, the pump being upstream of the selector valve will also pull fuel from the main and push it down to the engine and take out any air in the line downstream of the selector valve to the engine. So yes, you are right that the mechanical pump will struggle to clear the air as it tries to pull compressible air through, whereas the auxiliary pump has better head pressure of fuel from the main tank (provided it has fuel) to push down the line.
Thing to remember, even though it is called an auxiliary fuel pump, it only serves to pressurize the fuel line from the main tank upstream of the selector valve. Depending on how you move the selector valve, will impact where you send that main tank pressurized fuel; either to front engine, back engine, or off (when selecting aux tank).
I hope this clarifies...
Jeff
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