Even though both Bluetooth Classic and Bluetooth Low Energy both use 2.4GHz and GFSK, channel bandwidth and other parameters is different between them. So, they cannot communicate even at the PHY level and that means no.
Note that I use the nomeclature Bluetooth Classic because although Bluetooth Low Energy is specified in the v4.0 spec, Bluetooth Classic is also speced there. So saying Bluetooth v4.0 might confuse (although saying Bluetooth 2.1 wouldn't given that no BLE existed in that spec).
Bluetooth Classic was made for higher data rate applications (audio, headset, etc) whereas BLE sacrifices the data rate in order to lower power consumption. This rendered them incompatible.
Most phones support either Bluetooth Classic or Bluetooth Classic + BLE, but you are unlikely to find any phone/tablet only supporting Bluetooth BLE given that they need classic bluetooth for headsets.
Your post touched on another issue. Apple decided a long time ago that communications using Bluetooth classic for the interchange of data (not audio) requires the developers of the device to become part of the MFI (Made for Apple) program, which means adding a special authentication chip to your device. Without this device, it is not possible to send data between Apple products to Bluetooth classic. This doesn't apply to audio/music though.
The restriction above isn't present for Bluetooth BLE. iPhone/iPad/iPods with Bluetooth Low Energy can communicate to any device with BLE support without needing the authentication chip.