Hi John
Can I reflash the bootloader through the Arduino IDE with the ATMEL-ICE?
Yes you can.
But, the bootloader they use in the demo won't load on the Sparkfun SAMD21 Mini Breakout. It said the file type was incompatible. That got me confused that it was .hex vs. a .bin issue. But in the end, it must have been something else. Sparkfun doesn't have a .hex of their bootloader available and looked like I was going to have to compile my own. But, the Adafruit Feather m0 bootloader worked fine.
Your issue could be do with the fact that Arduino.cc and Arduino.org use different bootloaders. The Arduino.cc uses a modified SAM-BA bootloader for their Arduino/Genuino Zero, while Arduino.org uses the STK500v2 for their M0/M0 Pro.
The consequence is that the Zero and M0/M0 Pro are incompatible each other's IDEs unless you first burn the corresponding bootloader.