But would it be traced, the funds that got onto the new address, so to speak?
Frankolala did not answer your question correctly. Read what I posted above which is the answer that supposed to be given. Your coins can be traced on the blockchain unless you use some means to block the trace. Coinjoin is the best while mixers are also good. No KYC exchanges can also be helpful.
Thanks, I think I've slipped that detail out, I just never did such a process myself - and if it's done automatically (the funds just go to a newly created address, the previous one is drained, perhaps), how one may even try to hide the tracks..