Sorry about the silly question but is there a reason why you would want to protect a 120-277V LED driver with a fuse that is 600V rated? Does that really protect the device/driver?
The voltage rating is only a maximum rating for the fusing device. It has no effect on the functionality of the circuit. The fusing device can operate as specified up to 600 volts but may be used at any voltage lower than that. The relevant rating on the fuse for device protection is the Amperage.
Fuses that are rated for higher voltage (and maybe higher breaking current) have less tendency to arc, so they tend to open up faster and may be better for protecting semiconductors.
The manufacturer may have found, by actual testing, an "off label" use for the fuse that is cheaper and/or more available than one designed specifically for I2T characteristics.
If a fuse blows and you assume the fuse is protecting you from working and touching it then a power transient or lightning strike creates some 4kV spike, will you be protected? Perhaps with a 600V fuse but not with a 300V fuse. This is why fuses are rated much higher than the applied voltage. Even AC-DC supplies can fail with a feedthru of the lightning voltage.
Will the circuit be protected from arcing after the initial short caused the fuse to blow? This means your fuse becomes infused if the safe breakdown voltage rating is exceeded.
From my 1 to 10us pulse and HV testing experience I came to some conclusions about this. When fuses are rated for voltage this assumes RMS voltage withstanding not spike voltages. Becauase air ionization takes time for the miniature lightning bolt to be created it may be observed that the 1 to 10us transient breakdown voltage can be > 4 times the RMS. Transients < 1us will be > 10 times the RMS rating. Thus I might estimate your 600V fuse would withstand a 3kV transient of 1us and possibly longer. This is a common occurrence and the follow-ON effect is a crowbar or SCR ionization lightning bolt of current limited by the circuit resistance.
In the case of a primary fault blowing a fuse, the circuit might vaporize and trip the breaker. But if the fuse blow was merely an undersized fuse or a worn fuse with a functional load, the load might just flicker. I have the experience that in our cottage many years ago where the light switch must have arcced rated for a similar voltage near a lightning storm and the bedside tungsten lamp sounded like a flashbulb but just gave a short dim flicker of light.
The Follow-on current is often more harmful than the initial arc that triggers a gas tube or a broken fuse to arc. I recall a former senior colleague who designed an outdoor RF repeater powered by the grid had a gas tube for over-voltage protection and a lightning event a block away caused a 3" crater hole melted in a PCB because he was unaware of the negative resistance of ionization in a gas tube also in the air which acts like an SCR.