The kernel sources available often (read: almost never) actually match the currently shipped binaries (by which I mean, they're out of date).
I'm vaguely hoping they'd still lead to a booting device regardless, but it's hard to say without a serial shell

.
That said, any decent toolchain should do, the kernels are built by NTX, not Kobo, so they're never actually built with the same toolchain as Nickel.