No. HP Touchpad's USB port doesn't provide power to connected devices. This device (and any other Mass Storage device) needs some power to work, so it won't work with HP Touchpad, no matter what software is installed there -- it's a hardware limitation.
(1) "Out-of-the-box" with stock system software without any modification, using Media Importer App from Play Store, you can view/play files/video etc. stored on a MicroSD card (copied via a PC), but you can't write files to the card (when connected to Nexus). You have to use a PC to write files to the card.
See FAQ of the app: http://nexususb.blogspot.com/2012/08/faq.html
(2) Root the system, install Stick Mount or USB OTG Helper from Play Store, you can read/write MicroSD card using this reader, copy files between device's internal storage and the card -- like what you normally do on a PC.