It follows from Turing that you can not make a virtual memory system that never page faults (given non-unlimited physical memory, of course), partly because you can't fully reason about execution.
I'm not sure Turing says that at all.
In fact, I think it is entirely possible to have a virtual memory system that never page faults.
For example: The non-paged pool. Also Win32k's shared session data.
The Turing halting problem says you can't write a program in an also Turing-complete language that fully tells you whether or not the other program will do X or not do X. This is because if bool Halts(Program p) is a Turing-complete function, then this program defeats the logic: