As far as I know there are some studies reporting that broadband data transmission in rural areas decrease the information asymmetry between urban and rural areas. In my opinion not only broadband, all means of ICT diffusion have significant effects on creating information society.
While it may be true for more developed countries, where the affordability is not an issue in rural areas, broadband connectivity though very helpful does not seem to work as efficiently as other means like mobile telephony or the television in creation of a Information Society.
Assuming households can access broadband in rural areas (physically and financially), have the necessary hardware to send/receive digital information (computer/laptop/ G3/4 mobile phone), and have the necessary knowledge/skills/training to use the broadband technology, then inevitably they will become part of the information society. However, the question then becomes 'What will access to the information society do for them?' If all it does is allow them to download YouTube clips, post messages on social networks and send emails to friends and relatives, then this may contribute to improved quality of life (debatable), but is not effectively contributing to rural development.
A project is in progress in the highlands of Scotland (sparcely-populated with poor access to services, and few employers) to introduce broadband to rural communities - a project set up by staff at Stirling University. The aim of this project is to create jobs through use of broadband internet by households, working from home. It is too early to say what impact this project will have, but this is what broadband in rural areas should be targeting.