Can I call memcpy() and memmove() with “number of bytes” set to zero?

From the C99 standard (7.21.1/2):

Where an argument declared as size_t n specifies the length of the array for a
function, n can have the value zero on a call to that function. Unless explicitly stated
otherwise in the description of a particular function in this subclause, pointer arguments
on such a call shall still have valid values, as described in 7.1.4. On such a call, a
function that locates a character finds no occurrence, a function that compares two
character sequences returns zero, and a function that copies characters copies zero
characters.

So the answer is no; the check is not necessary (or yes; you can pass zero).