No, this kind of thing is ruled out by the protocol. There's a theorem called "monogamy of entanglement" which means that two maximally entangled qubits can't also be entangled (or even correlated) with a third. This means that Alice and Bob can guarantee that the key they're agreeing on wasn't intercepted. The theoretical argument is airtight. It doesn't rely on any assumptions about the adversary's computing power, or on whether the adversary has access to a quantum computer. The only way it fails is if physics works significantly differently to how we think it does.

Of course there can still be implementation errors or attacks at the endpoints. The strength of the chain is the strength of the weakest link. But the abstract protocol itself is a very strong link.