Short answer: Except for 911 calls, no.
Long answer: You can use it to make 911 calls, and you can use it to contact the service provider. That's it.
It's important to understand that 911 is very special and should not be abused. "I'm trapped on a lonely road and I need a tow truck" is not a valid 911 call, for instance. 911 is for summoning police, fire trucks or ambulances, and nothing else. This is not a joke. If too many people use it for trivial things, then it may not be available for the person who really needs it. (Do not call it just to see if it works, for instance.)
The phone can't be used for anything else, because of a technical aspect of how CDMA works, which was actually put in there precisely to defeat this sort of thing. (What it actually defeats is phone cloning: it keeps someone else from using your phone number to make calls with their phone, thus making you pay the bill for their hour-long calls to Mozambique or Paraguay.)
A CDMA phone uses something called the long code to spread the chip sequence that it sends on the RF link. This works because the cell and phone both use exactly the same long code, precisely synchronized. On the reverse link the long code is modified using the phone ESN. The ESN is never transmitted by the phone to the cell, so it can't be intercepted by cloners snooping on the radio link. Rather, when the phone registers with the cell, it sends its NAM. The cell system then looks this up in its database and retrieves the ESN from there. The phone itself also knows the ESN because it is stored locally.
Thus both the cell and the phone modify the long code the same way because they're using the same ESN, and the signal gets through.
A cloner could conceivably intercept your NAM, but if he changed his NAM to match yours, he would not meet with the same success. His phone would register using your NAM, but his phone would use his ESN on the reverse link. The cell system, on the other hand, would use your ESN on the reverse link, and they wouldn't match. Without going into too much technical detail, the effect of this is to substantially reduce the amount of signal the cell can derive from the RF with its rake receiver. Usually there's too little to reconstruct the bit sequence, and after missing a certain number of packets in a row, the cell will give up and drop the call. At best the phone won't work reliably, at worst it won't work at all.
Well, with your old phone that's exactly the situation. The old phone still identifies itself to the cell system using the same NAM as was originally programmed into it, but the cell system has updated its records for that NAM to indicate the ESN from your new phone rather than the one from your old phone. Thus when you try to make a normal call with your old phone, the ESN doesn't match and the call won't work.
This does not apply to 911 calls because 911 calls are special. The reverse link is not modified using the phone's ESN on a 911 call, so the call will work normally. Equally, a call to the service provider using a *-code is not modified using the phone's ESN, so that too will work properly.
But nothing else will work.
The only way the old phone could continue to work was if its ESN could be changed to match the new phone. But that's both illegal and extremely difficult to do. In fact, the phone manufacturers make it as difficult as they possibly can, because if you could do it then a cloner could do it, and could steal service and stick you with the bill.
Note: If a phone is dual-band or dual-mode, and thus supports AMPS, it is sometimes possible to force such an old phone into AMPS mode and to make a credit-card call. However, you can't rely on this, which is why it's not a good idea to store a deactivated phone for use as an emergency phone in a car. Even if AMPS coverage is available, the carrier may not permit you to make a call in that way.
(Another reason this is not a good idea is that LiIon batteries do not have a really long shelf-life; left alone they discharge themselves in a couple of months. When you need the phone, you might find that it doesn't work.)