Yup, that should work. My only concern is that the GFCI device you have linked may or may not trip on a loss of power. It doesn't clearly say and both are common.
I believe this one should maintain closed on a loss of power.
https://www.amazon.com/dp/B001OE3JHC/ref=psdc_6396124011_t1_B000XVG72G
“All Tower’s GFCI Adapters are designed to automatically reset to 'ON' position upon being plugged in or after a power interrupjtion. All automatic reset GFCI’s must be manually reset after a ground fault occurrence.”
EDIT: link
http://towermfg.com/gfci-adapter/