I actually looked into the ANT+ side a bit. There is a joint BT smart/ANT protocol stack, but it is downloadable from the thisisant website. I think, from memory, it is called S332.
It does however say that is is 'configurable' using BT. That makes me worry that it loses BT functions if the concurrent stack is used. File transfer is obviously the big one.
The specs include 8 ant channels I think, so it could possibly transmit 8 lots of data over different channels... Not sure. The current usb sticks can do eight channels, but this is a different chip. I have one of them. I think it is a NRF24AP2 & doesn't do concurrent BT. This looks better, but there is code on github that helps linking the NRF24AP2 to an Arduino and it has been documented as working. As the metrics are not standard it would be standard ANT rather than ANT+. BT already allows multiple profile over a single connection: for example the 4iiii viiiiva ant+/BTLE bridge allows power/S/C/HR over one channel.
The other thing I've noticed is that this chip can do BT central and not just peripheral. I have an Arduino 101 with inbuilt BTLE, but annoyingly it can only do peripheral, so I can't connect it to other peripheral devices.
If the hardware allows it there is also the possibility of Near Field Communication too. The chip on its own can do it. I haven't thought of a use for it though. Maybe if it used on a bike out could be used to unlock a D- lock. With two of them maybe they could sense each other, so they turned on fully when brought together e.g. one on each wrist. That I can imagine uses for.