No, because register $0 always contains a zero.
You may try to copy a value into it,
and the instruction will appear to execute correctly,
but register zero will not be changed.
The MIPS processor endlessly cycles through three basic steps. Each cycle executes one machine instruction. Everything the processor does is done by a sequence of machine operations. So, everything that a program does is the result of performing millions of machine cycles.
As execution proceeds through a sequence of instructions in memory, a special register, the program counter, contains the address the instruction that is next in line to execute.
Fetch the next Instruction. The program counter contains the address of the next machine instruction. The instruction is fetched from memory.
Increment the PC. The address in the program counter is incremented by four.
Execute the Instruction. The machine operation specified by the instruction is performed.
Why is the program counter (PC) incremented by four each time?