All damage from Magic Missile is part of a single effect, so the spell would have enough damage to overcome the damage threshold and damage the keelboat.
Even though there are different missiles flying around, Magic Missile is still just a single spell. Re-reading the Damage Threshold rules (emphasis mine), this means that the keelboat would take damage.
Big objects such as castle walls often have extra resilience represented by a damage threshold. An object with a damage threshold has immunity to all damage unless it takes an amount of damage from a single attack or effect equal to or greater than its damage threshold, in which case it takes damage as normal. Any damage that fails to meet or exceed the object’s damage threshold is considered superficial and doesn’t reduce the object’s hit points.
As further evidence that Magic Missile is a single effect and not multiple effects, consider its interaction with Shield:
An invisible barrier of magical force appears and protects you. Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack, and you take no damage from magic missile.
Notably, Shield says you don’t take the damage from the spell (notice the italics), not the projectiles/pieces of the spell.