To get GPS time it is necessary for your Android to strip the ephemeris data from a satellite NMEA data string. Currently GPS time is ahead of UTC by about 6 seconds.
You don' explain why you need such accuracy (Time posted from a satellite can be accurate to about 40 ns). To get this precision you need
to get a satellite fix, receive the data on your Android, and probably either compare the data with something internal or display the data on the device's screen. Your problem begins here.
AI2 graphics display on AI2 apps is inherently slower than display using apps compiled with Java compilers, the lag in satellite acquisition (this depends on the device location - in a parking garage or out on the highway makes a difference) and the time to parse the NEMA string all contribute to a delay in using the ephemeris information to displaying it.
If someone were to write an extension to receive the NEMA data, you would have access to GPS time information. How accurate would that data be? You are expecting an answer with less that +/- 200ms. I am not sure that is possible coding with AI2. Just pushing a button on your device will not provide the exact time of the touch. The cumulative affect of the 'delays' acquiring the NMEA string, processing it and displaying it will mess that up. If you do perchance write an extension, be sure to test it against an atomic standard
Check out
http://www.time.gov/ . It provides an accurate time standard corrected for network delay that might be appropriate for your use requirments.
Regards,
Steve