After some testing I conclude that using this feature DOES sign you in in such a way that it is shared with web pages you visit, i.e. it adds a cookie to your browser.
Sign out of twitter. Try the share button, it asks you to sign in. Sign in inside the share button. Visit twitter - you're logged in again.
Pity, it would have been a nice feature if it kept a separate cookie and enabled me to share when I want to share but disallowed the constant leaching of personal information that you get from being logged in to social networks.
They share cookies and other data like normal