No, it does not.
Your first statement is correct assuming the impedance of the two speakers is the same: 1/R = 1/Rs + 1/Rs.
But, in biwiring the impedance through part of the crossover to the tweeter will likely not be the same as the impedance through part of the crossover to the woofer: 1/R = 1/Rt + 1/Rw.
And remember that impedance varies with frequency.
More specifically, how would this work out?
My amp has two sets of switchable speaker terminals, "Spkr A" and "Spkr B".
If I single bi-wire, I'd have a single pair of bananas connected to the amp's Spkr A terminals, but which would diverge into separate speaker leads to go to the woofer and tweeter inputs of the speakers.
If I double bi-wire, I could connect one set of spkr cables from the Spkr A terminals to the woofers, and run a second set from the Spkr B terminals to the tweeters.
The Spkr A and Spkr B terminals are wired in parallel. If I were to connect 8-ohm loads to both pairs of spkr terminals, the amp would see 4 ohms.
So in this case, wouldn't my amp see a different load with double bi-wiring than with single bi-wiring?
Hold on, folks. It doesn't matter at all what the impedances of the hf and lf parts are and it doesn't matter whether you use single-biwires or double biwires or how many terminals there are on your amp.
If you connect everything to one amp, regardless of the wiring, the impedance load is the same as with single wiring.
OK, that is not too uncommon but the effect would be the same (if not worse) with the the woofer connected. Any woofer load would be in parallel with and, therefore, would lower the impedance even more.
Besides, the same amp is connected to both HF and LF, in parallel, even when biwired.
So, the issue has nothing to do with biwiring. It is just the usual question of whether an amp is stable with that load under any circumstances.
Any fisrt order crossover has drivers operating over greater frequencies. Drive a tweeter at 300 cycles and report back with your findings. Blown tweeter or amplifier?
A buffered or throughput amp has no connection with any part of a crossover as is "normal", so depending on how stable the amp is determines which blows/burns first. I have blown a Krell amp this way and can think of no other brand as stable at frequencies approaching DC.