If my computer has been compromised and the hacker uses software to obtain my ssd serial number or my graphics card serial number, can the hacker identify me?

..and what if this hacker is the police?

I know about the digital fingerprints windows uses to activate windows ect, but if the police were to hack into my computer not knowing who i am, could they then find the serial numbers on my hardware and order the companies that sold said items to me to reveal my identication?
I had a long discussion with a friend who denies that this is possible, i think it is very likely the scenario if the police hack me and find NSA hacking tools or bomb making scemes on my pc