I mean that's fine, but you are the registered owner 》renter of that domain, so you are linked to it in a database somewhere, even if your info is behind whoisguard-style obfuscation. Even if unlikely, should a dataset get exposed or the service stop functioning as intended, you're linked. No real worry for singing up for future junk-mail, but risks escalate when employment is at stake.
A sinister method is to state your birthday as Jan 2nd 1919. Just enough time to be remotely plausible. Bugs are sure to follow the account for the remainder of its existence.