No. I mean menu>settings>accounts and sync>background data. If this is turned off, then no app will access the internet unless you open them yourself. Of course this will prevent IM apps and email apps and whatever to update and notify you of any new event if you are connected.
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SugarSync and DropBox Referrals
SugarSync (gives 5gb free on registration)
DropBox (gives 2gb free on registration)
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