Sort of, it would disperse slightly over the range of its shot so if it was within 1km, no it would not disperse at all, but 1.5km to 3km it would start to spread out but not very much compared to a Scatter Gun and it would keep its long range.
Consider the Starfarer: It is 23.5m tall.
Consider the Arrow: It is 4 meters tall.
If the shot leaves the Ion being, lets say 15cm across, at 3km it only has to be 20 meters across to only hit the arrow with less than 25% force while still hitting the Starfarer with the full 100% force.
Additional thought on this in regard to comparing to Scatter Guns:
Scatter Guns have individual pellets each with a small amount of damage which scatter randomly with space between each pellet. If you can get all the pellets to hit the same target its one big slap as there are so many of them but if they spread out too much before hitting the target some miss and it's a much smaller damage delivered.
In my thinking for the Ion weapon, there would be no gaps between the damage deliverers, so calling it "Spread" isn't quite right - where there are gaps between the pellets of a scatter gun there wouldn't be on a long range spreading energy weapon. If you imagine the scatter gun pellets not spreading but staying next to each other and growing as they fly forward (retaining the same damage despite being bigger) that's sort of what I am envisioning.
To draw a picture:
Imagine this 10x10 grid is a cross section of the Ion weapons bolt/beam, with each box of the grid counting for 1 damage amounting to a total of 100 damage (to put a number on it, not actual numbers)
If the beam/bolt is only 1 meter wide, it will hit with all 100 points of damage the round has, as imagined in the below mock-ups, no matter the size of the ship - the ships are always large enough to catch the whole hit of all 100 points of damage:
(not to scale) damage grid 1 meter across
(not to scale) damage grid 1 meter across
If the above Starfarer has 300 health points and the arrow only 50 health points, the Arrow is one-shot and the Starfarer is only two more hits behind.
But lets now stretch that damage field to 20 meters wide as in my previous example with the spread of the weapon from 3km - the Starfarer is large enough to still catch all 100 damage points, but the Arrow is now missed by most of the damage points:
(about to scale) damage grid 20 meters across
(about to scale) damage grid 20 meters across
Although the grid is wider and the boxes bigger they still count for 1 damage each so the above Starfarer has been hit with the intended 100 per shot Cap Ship Killer punch of the Ion, but the Arrow has taken only 32 points of damage. It's still a reasonable hit at this angle for the fighter, but it's not a one-shot, its a survivable alpha strike which the Arrow pilot can then react to using the light fighters capabilities to their advantage to defend themselves. EDIT - Also, as the 3km shot is spread over the whole of the light fighter hull, each component takes less damage to its health pool too. Look at the Arrow above, the cockpit is only taking 6 damage, the wing only 4 damage. Not only would it be hit for less total damage, It would also be much more reasonably spread out leading to a survivable amount of damage taken at range. A large ship like the Starfarer would receive much more damage in the 40's to 60's per component because they are just so much larger. The nearer the Arrow got to the Ion, the more damage the Ion could pin to an individual component upping the chance of a one-shot in close quarters to a certainty if only the Ion pilot could hit the Arrow. - EDIT
Hope the above makes sense, this is how I reckon the Ion can be reverted back to its original Might against large ships while losing the Light Fighter one-shot ability but still able to deal damage to those little ships on a more reasonable scale at distance. It keeps the damage in scale to the intended big ship targets.
As it's spread over distance the closer the Arrow gets to the Ion the thinner that grid will be and the more damage will hit the light fighter as long as the shot is still on target, so it doesn't leave the Ion vulnerable by any means but gives the Arrow pilot a chance to counter it without being wiped off the map before they know what's happening.
Balanced keeping the ability to assault Cap and large ships from a distance while not being able to one-shot a light fighter from a distance? Sounds like it :)