http://www.onemanga.com/Naruto/441/13/Originally Posted by Pandadice
http://www.onemanga.com/Naruto/441/14/
There ya go.
If he hadn't known that the real one wasn't with them, he would have been fighting Pein as 6 different ninja, not realizing that they were all puppets controlled by the someone who isn't present.
Now then, without Konoha having the knowledge of the message of the real one not being with them, they would never have been trying to find information about Pein's identity from the capture rain nin or from the dead body. This: http://www.onemanga.com/Naruto/436/04/ would not have happened.
And after this: http://www.onemanga.com/Naruto/442/17/ they would have assumed that Pein was completely finished and left Nagato free to create more bodies and attack again later. But having the information allows them to go after Nagato to finish him off once and for all.
To sum it up, the "battle tactics" that are derived from the information are "I need to clear these puppets out my way first, then go after the end boss." Instead of "I've got to stop these 6 guys."