Does Eclipse kill a unit that has 4 or less Might?

No, the spell Eclipse does not automatically kill a unit with 4 or less Might.

Instead, Eclipse is a [Reaction] spell that gives a unit -4 Might this turn.

Whether or not the unit dies depends on its current state:

• If the unit has 4 or less Might: Reducing its Might by 4 will bring it to 0 or less. As established in Rule 143.2.b, a unit with 0 or less Might is treated as 0 for interactive purposes, but it does not automatically die.
• Lethal Damage: According to Rule 143.2.a, a unit is only killed if it has nonzero damage marked on it equalling or exceeding its Might.

Therefore, if you use Eclipse to reduce a unit's Might to 0, it will only die if it already has at least 1 damage marked on it. If the unit has no damage marked on it, it will remain on the board with 0 Might.