Battery backup for arduino

Would this work as a battery backup (power arduino from wallwart and charge battery, if power is lost from wallwart switch to powering from the battery until power is restored)?

Polymer Lithium Ion Battery - 6Ah https://www.sparkfun.com/products/8484

with LiPower Shield https://www.sparkfun.com/products/10711

Supplying power to the lipower shield with a Wall Adapter Power Supply - 5VDC 1A https://www.sparkfun.com/products/8269

I’m not quite sure that the LiPower shield will do this function or not… so I’m asking…