No the instruction sets aren't software. They are hardwired (dunno better word) into the CPU. Now a sofisticated programm might check if the CPU has an instruction set, and if yes, uses it. If not, it falls back onto the traditional, slower way of solving the same problem. Many programs though dont have those failsafes. A programmer may decide that without the predefined instructions his program can't function at reasonable speed and therefor foregoes supporting the classic solving-way alltogether.
Also instruction sets are mostly inheritated. A CPU that supports SSE3 also supports SSE2 and SSE1. There are exceptions though. For example the Intel C2D series supports an improved version of SSE3 called SSSE3 wich so far, no AMD CPU offers.
Right now i think pcsx2 need at least SSE2 to function properly. GSDX can be compiled up to SSE4 version. I'm not sure about backwards compatibility with the default download though.