The answer to this differs depending on the version of Bluetooth that your device is on.
For Bluetooth v4.0:
A peripheral cannot scan at all, whether in a connection or not. The peripheral can only send out adverts or accept incoming connections. For more information you can have a look at this document, page 18:-
http://chapters.comsoc.org/vancouver/BTLER3.pdf
For Bluetooth v4.1 onwards:
A device can be in central and peripheral role at the same time. By implication, this means that if a peripheral is connected to a central device, it can still scan for devices in it's "central mode". More information can be found in this link, page 5:-
http://www.ietf.org/proceedings/89/slides/slides-89-6lo-4.pdf
So in conclusion, if your device is BT v4.1 or newer, then this is dependant on the chip manufacturer, and if it is v4.0, then no, because the Bluetooth specification does not allow it.