EzCast | How to cast to a projector by connecting to it's Wi-Fi Hotspot and still keep internet Wi-Fi connection?
I think this works only if the projector is Wi-Fi Direct™
certified, and also if your android device support such capabilities. 

Wi-Fi Direct is a Wi-Fi standard enabling devices to easily connect with each other without requiring a wireless access point. Simultaneous Wi-Fi direct and network Wi-Fi is an optional feature for devices. Some devices allow this and some do not.

References


Can a device simultaneously connect to a regular Wi-Fi network and a group of Wi-Fi Direct-certified devices at the same time?
Android running Wifi Lan and Wifi Direct simultaneously
Wi-Fi Direct