Halfway so. On x86-64 with a recent enough glibc, there are multiple assembler versions of strcpy() using plain assembler, SSE2 and SSSE3, using the ifunc mechanism to choose between them: strncpy() has almost as many assembler implementations, lacking only a plain assembler one (indeed it uses the same code as strcpy(), with a tiny macro replacement). stpcpy() is similarly optimized. Furthermore, all three of these functions can be expanded inline in some situations by GCC, without calling down to glibc at all.
strlcpy() gets none of this. (However, a countervailing caveat: ome of the assembler implementations are so huge and unrolled that I'm not sure they don't cost more in icache hit than they gain in speed...)