Can I use the iOS device speaker output with Jam+, Mic+ or HypeMic connected?

No, when Jam+, HypeMic and Mic+ are connected to any iOS device they will always be the default input and output device.

Unlike Mac and Windows devices, it's not possible to select your iOS device speaker as a separate output when these units are connected.  

All output will be going through the device’s headphone output port which is controllable from the iOS volume buttons.

You can also connect Jam+/HypeMic/Mic+'s headphone Line output to any portable speaker with an Aux Line input using a 1/8" stereo audio cable.