Yes, it will probably work. But: Check your version number as well.
You see, I once had a PS1 with a fried mobo and another PS1 with a dead memory card reader. So I swapped the dead MC-reader for the healthy one, and it worked! Once. Then it started acting up again.
Both PS1:s were mark 5's -- SCPH-5502, so even though they were the same version, there were complications.
But working with a PS2 is just like working with a PC in general.
- Have you had any experience in working with PC hardware? If not, I can probably give you some recommendations etcetera before working with the PS2.
I would start by checking the version numbers on the back. Look for something like "SCPH-70004". You can also boot up the PS2 with a working mobo, and check the version from the boot menu (I think it could be done in "options").