The kernel can spin up a thread on the server side, but this works just like common thread pool libraries, and I'm not sure the kernel has any special role here except to optimize context switching when there's no spare thread to service an incoming request and a new thread needs to be created. With a purely userspace implementation there may be some context switch bouncing unless an optimized primitive (e.g. some special futex mode, perhaps?) is available.
Other than maybe the file namespace attaching API (not sure of the exact semantics), and presuming I understand properly, I believe Doors, both functionally and the literal API, could be implemented entirely in userspace using Unix domain sockets, SCM_RIGHTS, and mmap. It just wouldn't have the context switching optimization without new kernel work. (See the switchto proposal for Linux from Google, though that was for threads in the same process.)
I'm basing all of this on the description of Doors at https://web.archive.org/web/20121022135943/https://blogs.ora... and http://www.rampant.org/doors/linux-doors.pdf