Well, kind of, but I’m missing the link between the tweet and this plugin.
This plugin gives you the option to make your own coupon message which is displayed when the coupon is applied.
It would be possible (I think) to implement an option with this plugin that you can tweet that you have used a coupon at the store and how you much you saved etc, the name of the coupon etc.
But the tweet will be made before the purchase is completed since this plugin does not interact with the later stages of the order system in Woocommerce (only the discount/coupon part).
Is it something like this you are looking for?
edit: I just realized that what you are asking about might be the facebook/twitter message when using the ShareYourCart integration with Woocommerce?