As these are Fermi cards they might be useful.

Exactly which one; there are 4 versions:
144 cores 709MHz (GF106), 128Bit GDDR5 z.B. MSI GX780
144 cores 590MHz (GF106), 192Bit DDR3 z.B. Dell XPS 17, Alienware M14x
144 cores 590MHz (GF106), 128Bit DDR3 z.B. Schenker XMG A501 / A701 (Clevo W150HRM / W170HN)
96 cores 753MHz (GF108), 128Bit GDDR5 z.B. Lenovo Y570p / Y560p

Try the short tasks and see how you get on (if you actually have one of these). Keep an eye on temperatures and run time.

Manufacturers are allowed to make bespoke adaptions of some GPU's. You are right that there are two reference versions; 144core and 96core, but the frequency, amount and type of RAM are also big considerations. My quick search found 4 different specs from different notebook OEM's, but there are probably more. It's often the case that OEMs have a DDR3 version with a higher clock competing with another OEM's build that uses DDR5 but a lower GPU clock. Basically one cancels the other out or there is little difference in performance. However in this case there is one outstanding GPU:
My guess is that MSI's 144core version @709MHz with 1GB GDDR5 would be able to run tasks, and complete them in time, but you would really need to test it to know for sure, and I have no idea about the cooler and therefore reliability. I guess performance would be slightly faster than a GT240/GT340. As it's probably CC2.1 only 96cores would actually be usable here but 709MHz is fast for a Fermi notebook GPU.