Whever the phone uses digital or numeric signal over radio to communicate is not relevant. In both cases, if the phone or smartphone can locate itself, it will be able to transmit this position as part of the encoded data transmitted to the carrier when initiating the call.
But the problem is still: can the phone correctly position itself ?
The right answer is NO. In msot cases, even if it integrates the GPS receiver, it will be unusable if you are not in a location where you can receive at least 3 GPS satellites. This includes uses of your phone **inside buildings** or even outside in streets bordered by high buildings, that are hiding the signal.
So the best your phone will have is the last position recorded (if it's not too old).
If you phone got shutdown because lack of battery and you recherche it and then switch it on again, the phoen will have NO valid position in memory. This position will be too old.
So all the cell carrier will know is the location of the cell antennas that your phone can detect and the position of the antenna on which you are connected and authenticated to initiate the call.
If your cell phone can only detect a single carrier antenna, your position will only be known to be within the coverage radius of this antenna (this antenna position could be several kilometers/miles away from where you are with your phone).
If your phone can detect several antennas (often not more than 3, and most often only 2), it will just divide the radius of search by 2 or 3 at most (using triangulation) but this is still not an absolute precision because various terrain effects affect the signals of cell towers you can receive and communicate with. This often increasess the radius by several hundreds meters.
So if you have no direct visibility with the sky where you can track GPS satellites, you'll be positioned within a radius about 2.5 kilometers or 2 miles. It's not enough for emergency services to locate you rapidly.
If you just turned on your phone in a place where GPS can be received, your phone may also needs about 2 minutes to be fully located by receiving all candidate GPS satellites. Ig you initate a call in that time, your GPS position will still not be known and not transmitted to the carrier, so you'll be located only by the cell tower positions on which your phone has been authetnticated.
Finally, not all mobile phones have GPS receivers. Only smartphones have it always.
There are still lots of people not wanting to pay for a costly smartphone, and that also want to keep a cheap mobile phone whose battery will not be gully drained after just a few hours. Old mobile phones can still remain usable for a full week or more without being recharged.
Smartphones need to be recharged at least once each day, and often several times a day if you use it for data communications and if you are in a place with a weak reception of cell signals, or if you have turned on the Wifi reception, or if you have viewed a video on your smartphone. So people frequently have now a secondary phone in addition to their smartphone or tablet.
If people start having tablets, those tablets can do everything except performing calls. These people will want to dump their too costly smartphone and will want to keep only a basic mobile phone, without data communication (because data communications is lready in their tablet).
"Old" GSM/CDMA phones are definitely not over. They are still sold actively and there are still new models (and notably they are bought by emergency people, because of their MUCH better battery autonomy, thanks to absence of complex applications, or color display and embedded CPU/APU that constantly drain too much energy when the phone is on). Some models can keep their battery charge usable for a full month, even when you use it to perform one or two hours of calls each month with them (it is completely impossible with "modern" smartphones that constantly need to be plugged to a wire and that are absolutely not "mobile"!!!).
For this reason, we cannot still replace other commucation means by a smartphone on a mobile line. We still need a land line because smartphones will be frequently unusable. They can't even be switched on when they are plugged to a charger, if their battery is still too low, notably if your phone switched off automatically: you'll have to wait for at least half an hour.
If your life depends on a call to 911 emergency service, you'll certainly won't want to wait for an half hour after locating a place where tou can plug your discharged phone. You'll want to be able to use a land-line phone.
Same remark if your land-line phone service is just a VoIP service: if your cable or DSL or satellite modem cannot synchronize to the Internet service provider, you cannot perform any call.
And you'll want to be able to use classic non-VoIP calls over the analog land-line service which is extremely reliable (this basic analog service over land-lines should now be free for everyone and should be able to transport calls to any emergency service, without even having to pay for the call or introducing any coin in pay-phones. you should be able to use any line, even a line owned by someone else).
All ISPs and cellphone carriers should transport calls to emergency services, independantly of the status of the subscription. This basic service should remain available even if you've cancelled the regular subscription service (carriers shoudl not turn off these lines physically, even if you can no longer use them to perform calls to other destinations or receive calls because these lines don't have a public number; but emergency services should still be able to recall these lines even if they have no public number).
On a mobile phone or smartphone, you should be able to call emergency services from any accessible carrier (even if you have not sobscribed this one), using the best carrier you can detect in the location where you are to save battery power during such calls.