Let me try to explain. If you have a tweeter, then you have a crossover. The crossover does two things. It lets the highs ONLY go to the tweeter. It also lets ONLY the lows going to the main low frequency speaker. So, with a tweeter, your system is routing the highs to the tweeter and the lows to the woofer. The question then is, how much of the highs are taken away from your woofer?
To put it another way, my GK NEO212 is wired with a biamp feature, and you can wire it so that ALL the amp's output goes to the 212's, and NOTHING goes to the tweeter. You could say my cabinet is FULL RANGE to the 212's. I am not even using the crossover network.
Maybe you could tell me what cabinet you have and we could research where the crossover frequency is that's sent to your tweeter.
In short, YES, you could use an on/off switch. The only problem with that is, there would be some highs that would still be blocked from the woofer. It might not even matter. Cabinet model needs to be known. Generally, YES, you can use a switch. In my case, I knew I'd never use that tweeter, so mine's not even in the circuit, and neither is the crossover.