Does Android support the single-user mode runlevel? Since Android is powered by a Linux kernel it should support booting in single-user mode.

Which version of Android supports single-user mode and how is one able to start an Android device in this mode? Any references?
Single user boot is a feature of the init daemon (initd, like sysVinit) and not the Linux kernel. Since Android only shares the kernel with Linux and not the init process, a genuine single user boot can not be achieved.

Android has something that is called "Recovery Mode", but it's not exactly the same as a single user boot on an Unix system. The approach of recovery mode on Android is different because instead of trying to repair the bricked/broken system, on simply can re-flash the ROM or perform a factory reset, which will hopefully restore the systems functionality.

About the init used: Android uses just a script called init.rc, which gets started by the kernel and is used to start further services. You can view the current source of init.rc here. It supports no runlevels.