Is this speaker crossover design correct?
Many years ago (in my days as an EE student) I also messed with speakers and crossover filters. I remember using inductors with values measured in milli Henries, not micro Henries as is the case with yours.

So I think your inductors are at least a factor 1000 too small in value. Look at some typical crossover filter designs, for example this one. Note how all inductors have values of around a couple of milli Henry.

Will it work with a more sane crossover filter: very likely yes.

Will it sound any good: that depends on your standards. If you have low standards it will sound good. If you have high standards: don't waste your money on trying to build your own speakers. Buy some used speakers instead. Good speakers have been around for many many years. Decent speakers can be had for little money.

If you insist on building your own, then be prepared to experiment. Or get a pre-designed kit, that way you can be more sure the speakers will be a better match and the crossover filter will be tweaked for that combination of speakers.