If you do not use an electronic crossover, this approach has limited usefulness. It works better with transistors than it does with tubes though, as most speaker crossovers are high impedance when they are blocking the unwanted frequencies. This causes a transistor amp to make less power. It may not reduce the power of a tube amp all that much.
If you use an electronic crossover, the introduction of the crossover itself will have an audible artifact. How much has to do with the design, but no crossover will be completely transparent or neutral. In addition, most speakers have nuances of driver behavior which most electronic crossovers don't take into account.
So it can be tricky! My advice is to try it but be careful- the top amplifier outputs cannot in any way have connections to the bottom amplifier (for example- through the speaker's passive crossover), else you could damage something.