No. Your BBC iPlayer account asks for your postcode - https://account.bbc.com/account/settings - I *think* that was compulsory as I wouldn't have entered it otherwise..
Also they could find your e-mail address linked to your identity in other databases.. remember those 'e-mail age verification' things where they can tell you've over 18 from e-mail? it's probably because they cross reference your data in other systems.
I saw some suggestion online that they were feeding this data to TV Licensing - I actually asked directly from the data company they used as I recall and they claimed not to have any data on me..
(I can use iPlayer legally as I am in a household with a license which may have changed things)
I have a BBC account for BBC Sounds, not that I use it that often these days, but I use a postcode that is not mine and the email is a Yahoo one.
The people who have had emails saying they are using Iplayer when they say they don't have a license are those that uses the same email to register a BBC account as they used to tell the TVL they don't need a license.
I just don't tell TVL anything, I just let them carry on sending me letters, not that I use Iplayer, but I know someone who does and don't have a TV licence.
The other way is to use a different email address to tell TVL you don't need a licence to the one you register for a BBC account.
But Iplayer is certainly not linked to your licence.
Adrian
Desktop machines Mac mini pro with macOS Sequoia, also pc Ryzen powered with windows something or other.
Zooming with Zzoomm FTTP,