The pads on an intel processor can be cleaned off.
But, if the paste somehow got into the pins in the motherboard socket, then be very careful.
They are delicate and any attempt to clean them is likely to cause damage.
On ryzen, I think one could get the paste off of the processor if you are careful.
Alcohol will soften paste and dry up later. Use 92% if you can.
A non conducting paste on any part of a required connection may block a signal and not work .
Of course, prevention is the best thing.
Do not use more than a small rice sized drop.
It will spread under heat and pressure.
If the pins are on the processor, you can pour some alcohol in something and then put the processor in there and slosh it around, being careful not the hit the pins in the process. Hopefully it will be enough too get rid of it. As has been mentioned, Pins in the socket i.e. Intel, that is a whole other thing. Those things are very sensitive and it would take very little and the motherboard is toast.
I think that the mounting mechanism applying pressure to the cpu will cut through any paste that got into the socket. If there is a bit of paste in there that isn't conductive, leave it alone since trying to clean it out is more likely to bend the pins, it isn't going to short or fry anything.
If it were a capacitive brand of paste, then you break a sweat. It's a 'mare to clean out fragments of paste.
The cpu is easily cleaned with a cotton swab, no pins to bend on it.
the guy at the store told me that its impossible that a cpu can actually work with any of its pins even dirty. i was experiencing a buzz like sound, like cyber buzz every 30 min or so which was the source of my concern. then the guy told me it was the audio realtek drivers that cause that. i thought it might be my cpu pins hehe.
Not all pins are even active at any given time - some are reserved for features that your CPU may not have, so if those kinds of pins are dirty or even destroyed, nothing will happen.
Generally it's not a good thing though. I don't think they even make conductive thermal paste anymore so it shouldn't short, but it can cause bad contact. Either due to to the paste's insulation properties or because the paste is pretty thick and can cause some damage to the ultra-delicate motherboard pins.
So maybe nothing would happen, and maybe the computer won't boot, or maybe it will become unstable after a while or under heavy load...
It's unpredictable. If you are unable to clean the paste, then you can only hope for the best I suppose.
As for the buzzing sound, no clue, that could be anything but I doubt the CPU would behave oddly in such a specific way.