With a 24"x24" base cabinet you will only have an 1 1/2" countertop if you can find a sink small enough.

Personally I don't think it is doable. What about taking the cabinet apart and use it for skirting for the laundry tub?

I will practically have to take it apart to use it since it has a drawer and a shelf that glides out! DH suggested it, so I guess he's prepared to put the work into it to save us the $200+ it would cost to buy a cabinet!

Anyway, most sinks fit in a cabinet that shallow, as it is the standard base cabinet. Just wondered if SS sinks come that deep.

I'm not sure about where you are, but Australia and New Zealand homes have almost nothing BUT ss laundry sinks, often much deeper than 12" - a pity you can't seem to get them up here so much, and that some places seem to regard laundry sinks as optional. I plan to replace my side by side washer/dryer with stacking units so I have enough room for a laundry sink and a little cabinet of some sort...