At first I want to let you know that this question is not related with What is native implementation in Java. I got many useful information from that thread.
I want
Yes, see os::javaTimeMillis in /src/os/solaris/vm/os_solaris.cpp
to see the Solaris implementation for instance.
There are a few layers of wrappers to get there though, see JVM_CurrentTimeMillis in /src/share/vm/prims/jvm.cpp
Because the underlying methods are intrinsic to the OS you are running Java on, you will not find their source code in the JDK documentation. I suppose you'd need to find out exactly which procedures are called on your platform, and if source code is available for those (which strongly depends on your OS).