NO!
Once the buyer has paid sedo they will mail the seller his contact details.
It's then up to you to sort it out yourselves with Nominet.
Once the whois has changed the seller gets paid.
The reality is somewhat different to the impression you may get from their site:-
Domain Technical Transfer
Sedo works with both parties and their registrars to quickly and securely transfer the domain. Through our contacts with major registrars (Register.com, NetSol, eNom, GoDaddy, etc.) we can ensure the most efficient transfer possible.