No, the AES encryption key really never leaves the CPU, that is the whole point here.
TRESOR uses the four x86 debug registers to store a 128 or 256 bit key and then uses this key to calculate the AES round keys on-the-fly on each block of encryption using Intel AES-NI instructions. Also, they patched the kernel not to touch these registers at all. Therefore, after the initial loading of the encryption key, it never leaves the CPU again.
This approach also means you cannot use the ptrace(2) syscall anymore to attach to a program using a debugger such as gdb. However, if you don't want to debug a program, this proof-of-concept already works quite nice.
I noticed the PDF link to the paper on their site is broken, so please see the USENIX publication for details: https://www.usenix.org/legacy/event/sec11/tech/full_papers/M...