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This is really at the limits of my knowledge and I wouldn't trust it at all but I believe there are two types of Bluetooth 4.0/BLE module: one type supports only 4.0/BLE and the other that supports both BLE and 2.x/3.x.
I would however suspect that the mouse has support for only 4.0/BLE and even if it didn't battery life would be impacted negatively enough that you'd end up reaching for the dongle anyway.
Cheers.
I checked and my laptop shows the bluetooth as:
So it may not support the 4.0 / "Smart Ready" of the one I linked.