No. WSL2 uses it's own, minimal (proprietary) init, which basically launches default shell for the configured user and that's it. No service management in sight, and no equivalent of systemd's user scope or user session either.
That said, I've been playing around more and more with WSL2 on a secondary machine as a current primary Fedora user (for about 10 years now) and I really haven't found a good reason why I would need systemd in the WSL2 VM vs the custom init.
Most WSL2 users use it as shell to run occasional ELF/x64 binary that runs in console; for services, they would use Docker Desktop for Windows. Anything beyond that and you will quickly find out, that it is not really a standard linux distribution.
In practice that hasn't been a roadblock for me, because VMWare Workstation 15.5 finally supports running on top of Hyper-V, so I can have both working at once. Moving everything to a single hypervisor API has some nice benefits...
/s, obviously.