They address this at the bottom of the article (read the whole thing).

Battery removal can be equally deceptive. Even once one figures out how to extract the primary battery, there may be additional power sources within the apparatus. “Some phones use an additional battery for memory management; it’s unclear whether this battery could be used by logging and/or tracking systems such as Carrier IQ,” Mr. Harvey explained, referring to software that monitors mobile phone users.

Which is stupid because of how obviously wrong it is. Batteries that can sustain the cell radio, CPU, and audio DSP are not small and easily concealed, and more importantly tear downs of phones happen all the time and no such reserve power is ever found.

A greeting card can make audio recordings. The upload could be postponed until later when the main battery is reinserted.

(not saying that I believe that there's any way these phones are recording when the battery is removed, just that it is doable)

Sure, but those greeting cards typically don't have quad core CPUs in them, either.

You'd have to expand the claim to not only include hidden reserve power, but also hidden reserve memory, CPU, and audio system. Not to mention somehow convincing phone OEMs to actually spend the money adding this system to their motherboards and building it - there's no way in hell you are randomly sneaking that in at the factory without the OEMs knowledge. So now you also have to somehow keep the OEMs quiet about it.

In a word, "bull-fucking-shit".

Oh I totally agree that they're not doing it - it falls at the fact that as much power as the NSA has in America, there's no way they're convincing Korean and Japanese phone manufacturers to add a single penny to their BOM. I was just refuting the idea that it would be impossible to do.

I suspect the OP is claiming that Carrier IQ tracking could still be active, in low-power/sleep modes, that still could represent a privacy risk if the battery is removed. When the battery is re-inserted and/or the phone is turned on, then the data is transmitted to the cell tower, then Carrier IQ servers.

What would that be collecting when the main application processor and baseband processors are not powered? The battery referenced in the article is likely to backup a RAM chip and isn't even used in most modern phone/smartphone designs, which use Flash EEPROMs instead. There have however been phones which have a small internal battery powered by the external battery which has to be charged to operate the radio.

How do you take a battery out of an iPhone?

Easy: blender. Putting the battery back in is the hard part.

You put it in a faraday cage.

One of these bags is fine. (http://www.elcomltd.com/metsheildingbags.html)

Sure, this would block the incoming/outgoing signal. But last time I checked you can still hear your surroundings when inside a Faraday cage/bag. So unless you plan on permanently storing that phone in a bag I can't see how this would prevent a potential recording from eventually getting out.

Just to check:

Some people are saying that mobile phones have a second secret battery, and that battery is used to power the phone to record anything the microphone can hear, and then later when the phone has a signal and normal battery power that recording is secretly sent out to some secret spy agency?

Looks like someone didn't RTA

from the article:

Battery removal can be equally deceptive. Even once one figures out how to extract the primary battery, there may be additional power sources within the apparatus. “Some phones use an additional battery for memory management; it’s unclear whether this battery could be used by logging and/or tracking systems such as Carrier IQ,” Mr. Harvey explained, referring to software that monitors mobile phone users.

Mentioned in the article.