For networking, Kitura uses Kitura-net, which uses BlueSocket, which in turn uses C library's sockets[1]. On GNU/Linux, this is the GNU C Library, for which a package (Glibc) is provided by the Swift port[2].
For asynchrony they seem to be using libdispatch despite it being "early in the development"[3], but I've also noticed they're wrapping epoll and curl (see 1.B again), so it's hard to gauge the real extent of the hack.
You'd be hard pressed to find a Swift project that doesn't depend on Apple's proprietary Foundation because Swift needs it to talk to the world!
I don't understand what IBM is thinking.