As I understand it, Bluetooth in general (and hence BLE) uses a "client-server" model. A BT device is either broadcasting as a beacon or searching for them.
Is it possible to have a pair of BT devices operate as peers?
For example, make two devices (say smartphones) work both as scanning and receiving connections at the same time (preferably in background), for proximity-based app's purposes.
Yes since Bluetooth 4.1 devices may be in multiple states at the same time. Most newer smartphones support that.