Can bluetooth LE detect a touch using proximity?
The "proximity" feature in BLE is actually based on signal strength of the packets it receives  (RSSI). 

The RSSI changes very little with distance when the devices are far away, and disturbances play a large role in the RSSI value making it a very unreliable as a direct distance measure in the far field. 

However when you bring two devices close to each other (&lt;1m), the RSSI starts to grow exponentially and therefore the different disturbance play little role in the RSSI value compared to the distance.

While it is impossible to detect millimetre differences, i.e. plastic bits actually touching vs 1mm apart, you can get about 10cm accuracy when the antennas are near to each other. Please do note that this will be somewhat dependent on the antenna design of both devices, meaning to get very accurate you would need to measure the exact setup with the devices.