Short answer: Most likely not. It's up to the manufacturer to provide you with that data output on the cellphone, and they have no incentive to do so, and actual reason not to.
Long answer: Most likely not. The cellphone GPS is really not a full GPS, only partial (because it's designed to need to work indoors as well when you wouldn't get a GPS signal)... It uses a system called "Differential GPS" which basically means that since the cellphone towers are stationary you can know with extreme precision where these towers are located. Since GPS signals have a great deal of error in them you can use this method to reduce the error.
Normal GPS recievers attack this problem by combining the output from multiple GPS satellites and then calculating what a possible total error correcting value might be. Unfortunately even with several satelites because of the great deal of distance travelled for the signal it's difficult to reduce the error unless you already know your position, but then if you do it's pointless to use GPS, isn't it? If there was only some way to know what the error correcting factors were already for the GPS signals, then you could correct each one individually and come up with a very accurate position.
Enter Differential GPS. Since the cellphone towers are in a fixed position they use the information that they already know on their location to attack the problem backwards: They can determine the error in the signal because they already know their position. By combining this with the signal that the cellphone recieves you can reduce the innacuracy of your calculations greatly.
This is a long winded way of saying that it's not a normal GPS in your cellphone. IF the above method fails because you can't get any GPS signal on your cellphone (which will be frequent even outdoors) they have to rely on signal strength from multiple towers (because with digital cellphone technology all signals much reach the tower at the same strength, so the cellphone has to adjust it's broadcast power to compensate for distance, thus the cellphone has to know how far away from the tower it is). If you have more than 2 towers then you can triangulate the position the old-fashion way. Even if you only have 2 then you have 1 of 4 locations where the person could be (since we are talking about spheres here), but 2 will usually be either in the middle of air or ground.
In any case, the cellphone has to do a lot of calculations here to determine the position and thus you aren't going to find an NMEA compatible cellphone ... Additionally since this data is meant only to be accessible to the cellphone providers to track your location (er, I mean to pinpoint your location in the event of emergency, yeah that's it) it's not in their best interest to provide that data to you.
Read up on differential GPS here.