I have exactly same HP Probook 6570b with HM76 Chipset.
I just upgraded CPU to i7 3720qm and it started without problems and doesn't heat up too much either - only around 90-92 degrees Celsius under full stress.
All 4 cores and 8 threads are recognised.
I didn't even update BIOS, its F.62 version from 2015.
Actually, its on the official list as only working with EliteBook 8570p and not with probook in question. So it's still 4 core cpu within probook that officilly should not support it.
And there is very little difference between 3720qm and 3840qm.