Using a LiPoly Backpack with a battery + Uno?


I want to run an Arduino inside a device, using a LiPo battery. Since it's embedded I also want people to be able to charge that battery via USB when it's not in use. I found the LiPoly Backpack from Adafruit which seems perfect (Adafruit LiIon/LiPoly Backpack Add-On for Pro Trinket/ItsyBitsy : ID 2124 : $4.95 : Adafruit Industries, Unique & fun DIY electronics and kits) but I'm confused as to how it would work with an Arduino, as it's designed to plug into the Pro Trinket and charge when the Pro Trinket is plugged in.

From what I gather the backpack has a BAT pin and a 5V pin, and if the BAT pin is higher (ie there's no USB connected) then discharges the battery. Therefore I imagine that if it's attached to the USB breakout and it's plugged in/not plugged in the same logic applies, but I'm not sure if I'm missing something here, or misunderstanding how it works.

My question is, would the setup below work for using this with an Arduino Uno? (I'm using a USB breakout because it would have to be accessible from outside the enclosure.)

I would just buy a LiPoly backpack and try it out, but since I live outside of the US/Europe shipping is really expensive so I'd rather make sure it's actually what I need.

Thank you so much for your help.!