You should amp the components as a set, but you don't have to do it separately. The crossover also benefits the mids, not just the tweeter, as it keeps the mids from trying to go too high or too low as well. They are made differently, with different rolloffs so that they should blend smoothly with that specific tweeter, with the assumption that the tweets are installed in a good place as the mids.
If you have a component set already you should just keep it the way that they recommend. Usually this means from the amp, it goes to the component set's crossover, and then the crossover wired to both the tweeter and midrange. If you have an inline crossover (no little crossover box) then you should keep it as is.
The crossover will help block out the frequencies for the speakers to help protect them and divide up the sound for better speaker response (tweets not trying to play lows, mids not trying to play highs). That is why it's easiest to use the given crossover rather than amp them all separately and try to use the amp's internal crossover yourself. At most, if you have an amp, you'll just set it to hi-pass just in case, but I don't think it'll make a difference. The next thing is just not to overpower the speakers, and you'll be fine.
Hard core audio people feel that the best control is with amps to each tweeter and mid, so that they can control the gain/loudness of every component as well as the frequencies played, either with an EQ or the amp's own x-over. This is because they might like the sound of the mid, but not the highs, etc, so they want it "perfect" to their ear that all being opinion. If you really wanted to try it out, I'd say go for it, but might as well try the recommended way first, cause:
1 you'll save yourself two amp channels to power other speakers!
2 the box will have the total RMS power of the speaker components, but if you don't know the RMS of the mids and tweets separately, you'll have to ask and find out.
3 there's no guarantee it'll sound better separately amped.
Regards,
Jon