Can't they do that anyway,from stationary installations? I believe something like that narrowed the search area for the Kim family. In their case, I think they used their phone, recording data that eventually put the searchers in the right ballpark...
Yes, kinda, sorta, maybe, sometimes fairly accurately, sometimes only a rough location. It depends. These days it is referred to as "cell phone forensics".
Each of those vertical looking things one sees on a cell tower is an antenna, that covers a certain angle or sector. If the phone is detected by several towers, it is possible to triangulate between those antenna and get a position. With more than one tower receiving the signal, I believe they can also do a triangulation, of sorts, using the relative signal strengths received by each tower.
Additionally, using GIS technology and a digital elevation model (DEM), they can tell which areas are masked by terrain, where the phone
is not located, which is also useful information, especially if combined with other data.
However, in areas with minimal cell coverage, the phone may only be hitting one tower. In that case, often the best they can do is say
"it's over that way, somewhere" or words to that effect.
There are, of course, privacy issues involved. However, here in Alaska, the State Troopers have worked out regulations/procedures/policies with the cell providers so that in an emergency SAR situation they can quickly get whatever location information that can be derived in a particular situation. It is important that these regulations/procedures/policies are in place in advance, since some of this cell tower data is not retained by the providers for more than a couple of days. I suspect most areas in the country have worked out similar agreements.