That box is a crossover. It seperates high freq. sound from low. If you currently have no major problems with your existing speakers, and are just swapping them for superior replacements.. then it would definitely work using the existing harware LPF/HPF.
However, the older/standard speakers probably do not support the same range as the new pair. As a result, the old/standard crossover will no doubt be wired to parse frequencies suitable for the speakers it came with.
Space is more often than not the issue with crossovers, i.e. where the hell can i secure them? I've not taken a Leon door-card off.. sorry, but I'd imagine you're not spoilt for suitable spaces.
How about a smoke-test? Wire your new mid and tweeters to the existing crossover wiring and give it a listen. If you're unimpressed or undecided, go ahead with an "out of the case" sound test with your new crossover.
The vast majority of crossovers come with terminals for different configuration patterns. One that supports higher-freq. notes parsing than the other. Almost certainly a feature not supported by any standard system I've encountered. So there are benefits to using the new crossover. (Assuming it comes with a choice of connecting alternatives).