No, the key negotiation occurs between two clients.
In the Magic Wormhole protocol, the number at the beginning of the Magic Wormhole phrase specifies a "nameplate" used to negotiate the "mailbox" which both clients (sender and receiver) use. If a recipient specifies a _matching_ nameplate but a _non-matching_ key phrase, the file transfer transaction between the sender and receiver with a matching nameplate will fail (since they cannot correctly produce a shared key), but nobody else is affected in any way.
An evil attacker could DoS the magic-wormhole mailbox server by spamming mailbox nameplates with bad keys, since there isn't much entropy at all there, but they would affect only single transactions at a time.
In the Magic Wormhole protocol, the number at the beginning of the Magic Wormhole phrase specifies a "nameplate" used to negotiate the "mailbox" which both clients (sender and receiver) use. If a recipient specifies a _matching_ nameplate but a _non-matching_ key phrase, the file transfer transaction between the sender and receiver with a matching nameplate will fail (since they cannot correctly produce a shared key), but nobody else is affected in any way.
An evil attacker could DoS the magic-wormhole mailbox server by spamming mailbox nameplates with bad keys, since there isn't much entropy at all there, but they would affect only single transactions at a time.