All I can do is venture a guess as I have no data or proof to back it up.
For what it is worth, the reed modulates the flow into the instrument and in doing so drives the acoustic resonance.The reed lift is caused by flow and flow is reduced as the reed press down. At steady flow, the reed will flutter and oscillate flow.
The acoustic resonance, once started modulates the pressure sensed at the reed flow outlet. Whether this influence is strong or weak is hard to say though.
The reed flutter would depend on the flow, so if pressure fluctuation at the reed outlet is strong enough to affect flow, then yes, how strongly the reed flexes should be affected. I do not play any instrument myself, but I imagine one should be able to sense this effect when playing if this is the case.
The reed natural frequency, my guess, is more affected by its boundary conditions, i.e. how it is held in the mouth.
Just my 2 cents. We have to wait and see what more learned colleagues can offer in terms of advice on the matter.
Opening and closing toneholes can be understood as a variation in length of the resonator (in a very simplified way), and therefore the resonant frequencies that can be supported by it. Woodwind reeds couple with their resonators in an inward-striking fashion, but can only oscillate at the aforementioned resonant frequencies. If you calculate the input impedance for a specific finger configuration, you will find that it changes every time, and not only in the amplitude of its peaks, but in the pitch of its fundamental and consequently all of its successive harmonics.
Quoting the Handbook of Acoustics by Malcolm J. Crocker, on page 1287: "The reed in a woodwind instrument is a pressure-controlled valve that is closely coupled to the air column resonator, which determines its vibration frequency."