Blindly, I say it can be somewhat traced by it's MAC number since big manufacturers purchase/reserve MAC numbers in blocks. This allows determining what the laptop is, but not necessarily which individual one it is from a specific company unless they kept really good records of each and every computer made, like Dell and their service tags that seem to know all about your computer.
It gets a bit fuzzy on some individual cards sold separately. Boatloads of e-waste goes to China for "re-processing" and that includes network cards with their MAC numbers within that get re-cycled into a so-called "new" product.
So the final answer is... Yes, we can find you, if you have Java enabled.