strcpy() isn't part of libgcc. What happened is that without -Os, the compiler will inline certain invocations of strcpy() as a builtin.
What other builtin functions do we need to be worried about?
All of them. You have to provide all C library functions you use; there is no guarantee that GCC will inline any of them. Builtin functions like this are purely an optimisation, and the compiler makes choices based on if the tradeoffs involved make the inlining worthwhile. With -Os, it won't inline much, but it will still do some.
Segher