I read that the iPhone 4 couldn't do this. Is that still true of the 4S when used in CDMA?
As @Jannemans points out this wasn't possible in any CDMA phone until one point. But the question is valid now that the CDMA standard allows it.
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The limitation of simultaneous voice and data is not one of the iPhone but one related to the CDMA2000 standard.
However, the official CDMA Development group announced the CMDA X standard on Aug 17 2009. This standard allows for simultaneous voice and data:
Quoting the press release
A complementary device enhancement known as simultaneous 1X Voice and EV-DO Data (SVDO) will also become available during the same timeframe and will enable CDMA2000 devices to access EV-DO packet data services while in an active 1X circuit-switch voice call. For example, users will be able to send emails or access the Web while on voice calls; phones with GPS can update maps or download real-time traffic information while on voice calls, etc. This device enhancement, which enables these concurrent voice and data services, is independent of the air link standard and infrastructure.
When Verizon or any other CDMA carrier will implement this, is an entirely different question...
According to Apple, "CDMA networks do not support simultaneous voice and data over any connection."
I tried this with a Sprint phone, it didn't work. It gives an error message when you try to surf the web when on a call. However WiFi data still works.