"using the Arduino IDE, I'm assuming that the fuses are only set by the IDE when burning a bootloader" Correct. I have several boards with no FTDI header, only ICSP. I burn a bootloader first to set the fuses for normal 16 MHz operation, and then use File: Upload Using Programmer to put a sketch on with no bootloader. Biggest problem: forgetting the bootoader first and then getting reduced speed operation (1 MHz default).
MKii does not provide power, it senses the supply pin (6) and adjusts levels accordingly. Should work with 1.8V:
"•Programs both flash and EEPROM
•Supports fuses and lock bit programming
•Upgradeable for future device support
•Supports target voltages from 1.8V to 5.5V
•Adjustable ISP programming speed (50Hz to 8MHz SCK frequency)
•USB 2.0 compliant (full speed, 12Mbps)
•Powered from USB, does not require external power supply
•Target interface protection
•Short-circuit protection"