Yes! You are correct.I think omishra's post says otherwise.
At the Amplifier output, your have a complex audio signal duly amplified to power the speakers. So mixing, muddling, superposition of sound etc already taken place there because you did not amplify signals separately.
Now only thing remains how this is transported till crossover starting point before each driver. From that binding post to crossover entry you connect good wire - single or bi-wire, theoretically does not matter. But there is an assumption. I hope you are going to use wire with proper electrical properties.
When crossover filter receives that signal it just reacts to allow passage or resist. So IMO it does not matter if it takes signal from one trunk or separate wire. You are already feeding mixed signal.
If you are thinking there could be any push pull effect on wire due to driver sucking current then it could be during bi-wire at amplifier binding post too. But this could not be unless underpowered amplifier.