Maximum Data Rate on BLE Dual Mode Device
I can not answer with certainty, but I'm working on a project that uses a BT dual module (cc2564). The module works with both connections BLE and BR/EDR simultaneously and although I have not sent very large amounts of data in BR/EDR mode, I had no problem with transmissions. So my answer is that it is possible that the module (in my case the cc2564) may be working as BLE and can switch to BR/EDR mode to transmisitr large amounts of data.

I wanted to put this answer as a comment, because is not a proven response, but I haven't enough points to make it, and I think that maybe you want to know this. Sorry for that.