Can you use the M4 with that 6620? Yes.
However, you're using the PSU in a manner wor which it was not designed, and as such you have to jury-rig the PSU.
There are guides on here to make an ATX power supply do what you need.
This is not a setup I would recommend. MP3Car recommended the Carnetix, and I would, too.
If you want a case for the M4, get to fabricating.