Yes! Users would rarely follow the same brand on a number of networks. By reposting the same content, you reach more people. Besides, it leads to network integration: users might find your content on Twitter and later post it on their Reddit/Tumblr/etc page. Moreover, you can post the same content on the same network multiple times, just in case your followers haven’t seen it the first time. A life of a Tweet, for example, is only about 5 minutes. So only by posting it 3 or 4 times (on different days and different hours) you can be sure that most of your audience have seen it.