No. As explained in the SO answer, the worry is that the enemy will have been able to decrypt one or the other of your messages, at which point the identical underlying plaintext will help them crack the second cypher.
‘Crack the cipher’ in this case most likely meaning: figure out the daily code word key you are using for that cipher.
If they have already gained the ability to decrypt today’s messages from station A in cipher A, and can therefore recover the plaintext of those messages; if they then find a message of the same length sent from station B in cipher B they can guess that that might be the same message, reverse engineer the key and maybe then decrypt all the messages being sent from station B in cipher B today.
Bletchley Park employed linguists alongside cryptographers, and the linguists would help permute the messages (substituting German words for common abbreviations, for example) to mount these sorts of attacks.
