Avoid Logjam TLS Attack? As the Logjam attack allows a Man-in-the-Middle attacker to downgrade vulnerable TLS connections to 512-bit export-grade cryptography by modifying the ClientHello and ServerHello, can the Logjam attack be avoided by verifying the integrity of the ServerHello?
Downgrade attacks can be detected when the FINISHED messages are exchanged and verified. Of course, the goal of an attacker is to downgrade the security of the handshake, being able to compute the master key. If the attacker computes this key before both clients proceed to verify the FINISHED message, then he's able to spoof it and trick Alice and Bob.

Pointing to your question, that includes the ServerHello message, as the server would check if the messages received by the client match the messages sent by the server. In the case of a downgrade, the server detects that something different has been sent to the client, as there is a missmatch in the verification of the FINISHED message.