Disconnect the woofer

There would not be any energy consumed, since there is no driver to drive.

Many crossovers have a simple 1st order Butterworth section(an inductor) in series with the woofer Some let the woofer's natural inductance roll off the mids/highs. If there's more than that(a cap to ground after an inductor, balancing or EQ circuit resistors/caps/coils, etc), you will experience some loss/signal degradation. What's the low freq circuit of the x-over look like? A X-over that's designed for bi-amping/bi-wiring separates the entire hi/low-end section, via removing it's jumpers. If you can trace the low freq circuit of your x-over, and clip the positive circuit at the input terminal, you'll not have any further concerns.

I agree with Rodman. It depends on the crossover configuration. If it is more than a first order crossover (i.e., an inductor in series with the woofer), you would want to open the INPUT to the low frequency part of the crossover network, not its output which is connected to the woofer.

Regards,
-- Al