You can do something like that, but with a caveat.
In some cases systems "thrown together" like that will sound acceptable or even right, but you can't count on that.
The problem is potential gain differences. Yes, you can connect two amps to two preamp outputs, that's not the issue. But most likely they will have different gains. While the VK-200-s gain is rather predictable 26dB, the gain of the tube amps will depend on your choice of output taps and your load resistance. You can have pretty broad range of values depending upon your configuration.
All that means that if you got lucky by simply putting everything together - pop a cork, otherwise, you will need some means of gain adjustment... this is something the crossover box normally does for you. Without it you would need to make or purchase an adjustable attenuator.
Regards,
Victor Khomenko