Of course one might argue that the ability to get things done quicker means that people with higher speeds spend less time online, but this certainly hasn't been the historic outcome - in the UK in 2006, broadband users were spending 60% more time online that dial-up users, for example.
I don't want to overstate my case here - there's lots of factors that drive hours spent online, and it may be that some combination of these represent so much 'noise' that they are masking a positive impact from higher broadband speeds. However, that in itself is interesting - it suggests that even if higher broadband is important, it is readily swamped by these other factors.
The above finding regarding time online is also consistent with evidence that broadband speed makes no detectable difference to the economic impact of the internet across a range of European countries. (See p4 of this)