Can an iPad be charged while acting as a USB host?
Personal experience, I've never it.

But USB specification actually has defined such standard, under USB On-The-Go (OTG). A connector named Micro-AB plug will allow a device to be charged and enter host mode. This is also mentioned here on another Stack Exchange site.

Back to the question, is it possible? Probably no. According to this Wikipedia article about Lightning. A lightning-enabled device can act as host to power accessories or as client to be charged, but it uses either...or, so not at the same time.