I wouldn't. In fact I would stick with 512^2. I have noticed a significant performance improvement going from 1024 to 512. This is on a Droid 2, which I consider a good middle range device. Even if the device can support the size it can be very expensive to sample that texture, especially with filtering. Just getting it into memory is only half the battle.
You could store multiple resolutions and then query the maximum texture size and choose appropriately. You could even make it a user controlled preference. Just remember that maximum texture size and best size for performance are different things. Be sure to profile. You might be surprised where your bottlenecks are. I was.
Josh