Yes, and not only that, the pickups plus the preamp play most of the part on the Wal sound. The pickups have individual humbuckers for each string and the preamp combines these humbuckers into their designated Filters. It's the combination of those things, plus, body construction (mainly the neck) and pickups placement, that make Wal, well, Wal.
The closest you can get, electronically wise, is to use the multicoil pickups with the coils properly wired together with a preamp, like the Lusithand double nfp special, which combines the individual humbuckers, like a Wal does, into the filter preamps.