Is it possible to use a Microchip PIC32 as a USB host and device at the same time?
The USB can either be in device mode or in OTG mode.  You cannot have OTG on the same USB bus as a host like a computer.

Multiple OTG devices can switch between host &amp; device mode using "HNP" (Host negotiation protocol) but you can't do that with a pure host.

You would need two separate USB busses - one between the PC and the PIC, and one between the PIC and the devices.  I don't think there is any PIC device that has 2 distinct USB interfaces.

I would suggest using a second device along side the PIC32 to act as a USB device to connect to the PC, and use the PIC32's USB in OTG mode to talk to the devices.  This other device could be as simple as a FTDI chip to talk to the PIC32 through RS232, or something more powerful like another PIC (maybe a PIC18 with USB support) so you can talk through other protocols like I²C or SPI.