Yes, but since much of the code is not from your program single stepping is less interesting.
Here is SPIM with the example "hello.asm" program. The simulated console is in the background. In the forground window you can see the initialization code for the trap handler. If (in your actual SPIM window) you scroll down the forground window you will see the code corresponding to the source file "hello.asm". If you look in the DATA section you will see the ascii codes for the string.