Within a single function, an array could be held in one or more registers, just so long as the compiler is able to produce CPU instructions to manipulate it as the code dictates. The standard doesn't really define what it means for something to "be" in a register. It's a private matter between the compiler and the debugger, and there may be a fine line between something being in a register, and being "optimized away" entirely.
In your example, the parameter is a pointer, not an array (see dribeas' answer). So it would be unusual that the array it points to could possibly be held a register. The "main" architectures that you probably deal with don't allow a pointer to a register, so even if the array was held in a register in the calling code, it would have to be written into memory in order to take a pointer to it, to pass to the callee.
If the function call was inlined, then better optimizations might be possible, just as if there were no call at all.
If you wrap your array in a struct, then you turn it into something that can be passed by value:
struct Foo {
char a[4];
};
void FooFunc(Foo f) {
// whatever
}
Now, the function is taking the actual array data as its parameter, so there's one less barrier to holding it in a register. Whether the implementation's calling convention actually does pass small structs in registers is another question, though. I don't know what calling conventions do this, if any.