That depends. Microcode tends to be used in CPUs rather than regular ASICs and not all CPUs have re-writable microcode (though quite a few of them do). So unless you're talking about a CPU the answer is probably 'no'.
You probably have a bigger chance that there is an FPGA on board that you can re-load.
You probably have a bigger chance that there is an FPGA on board that you can re-load.