I expect the pressure to drop insignificantly below the vapour pressure when you extract the liquid, because bubbles can form, and these are very efficient to vaporize the liquid.
The potential drawback I see (which is a prohibitive annoyance in rockets, maybe not in your application) is that the liquid extracted from the tank is at saturation pressure then, so t's ready to boil at any point and time. Especially, it will cavitate in the pipes. Unless you have meters of hydrostatic pressure between the outlet, the pipes and the boiling surface.
The standard answer against cavitation is an overpressure in the tank, exceeding the vapour pressure, hence obtained by a different gas or by the same gas but heated.
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When pumping the liquid in, without venting, you'd need to be absolutely sure that there is zero amount of nonsoluble gas in the ullage. Such gas (air...) staying above the liquid would reach any pressure unrelated with the vapour pressure as it gets compressed.
Cryogenic gasses have it easier there, because most common gasses liquefy or solidify before, for instance, 77K.