No, that doesn't change the prospect of a CPU the system cannot identify working (or not working), and it doesn't change the fact that the 2960XM draws far more power than the voltage regulators on the board were ever designed for (and that's when they were brand new, not over a decade old as they are now). There is no harm in trying, but I wouldn't spend much on the CPU as your experiment has a far higher probability of failure than it does success.  Either way, report your findings back -- someone may decide to try the same experiment.  
i wonder if i can upgrade my CPU to Intel Core i7-3940XM or not
Dell latitude E5520 CPU replacement compatibility