Not exactly, but something similar has been tried (and successfully so) in the UK
The device wasn't an android phone though but rather a dedicated GPS-based driving telematics device.
We don't know for sure whether his evidence would have been accepted though as in this case when the accused said he had evidence from the telementics device the prosecution declined to present any evidence. As his solicitor put it:
"Based on previous experience in other cases, laser speed detection devices can produce erroneous results and in this case Mr Herron was convinced he was not speeding as alleged and stated he had telematics data to support that view. When confronted with failings in court the prosecution determined to offer no evidence."
This doesn't really set a legal precedent that "GPS beats Laser speed gun" though - because the CPS chose not to present evidence.
As others have commented though there's quite a few potential pitfalls with doing this - GPS data carries a certain level of uncertainty, it's pretty accurate these days, to quote GPS.gov:
GPS-enabled smartphones are typically accurate to within a 4.9 m (16 ft.) radius under open sky. However, their accuracy worsens near buildings, bridges, and trees.
and specifically for speed measurement:
As with positioning, the speed accuracy of GPS depends on many factors.
The government provides the GPS signal in space with a global average user range rate error (URRE) of ≤0.006 m/sec over any 3-second interval, with 95% probability.
This measure must be combined with other factors outside the government's control, including satellite geometry, signal blockage, atmospheric conditions, and receiver design features/quality, to calculate a particular receiver's speed accuracy.
The thing is there's going to a big range of accuracy in what a phone can offer - does it have A-GPS, GLONASS, how good is the GPS antenna, where is it positioned in the car etc etc. A lower end device shoved in the driver's is going to offer significantly worse accuracy performance than a top end handset sat in a cradle with clear line of sight to the sky.
In short it's a long way from being some form of get-out-jail-free card you can use in defense of speeding allegations. And it certainly gets it wrong often enough that you wouldn't want it (at least not in it's current form) to be the final arbiter. More than a few people have been dinged by their insurance companies when the supplied GPS tracker has accused them of driving beyond the limit when they haven't!
