I just had the time to measure the voltage my meter applies to the circuit when connecting it the same way as before. It was -1.1 mV DC.
What about AC?

I want to know whether it's worth it investing money in replacement caps (which, as I now know, were indeed the original problem)
If some current went through the CPU and damaged it, your capacitance measurement possibly wasn't accurate and you really don't know.
If your measurement is accurate, no current diverted to the CPU and the CPU is good.
If you feel like replacing the capacitors anyway, pull one out and test out of circuit. Even removing the CPU from the socket will still not remove the VRM.
Or run your capacitance meter into a scope (while measuring some actual capacitor) to see the exact waveform. If it's very low, chances are that you can use this meter in circuit without serious error and without damage to ICs.
The caps may also be bad by having significant ESR but capacitance mostly in spec.