Yes, stuff can unlock traits for particular units.
<GameModifier>
<ModType>Unit</ModType>
<Attribute>UnlockUnitAbility</Attribute>
<StrVal>Fire1</StrVal>
<Provides>Grants the Fire Apprentice ability</Provides>
</GameModifier>
To make an equippable item give a unit a trait is a little more complex but it is doable. First consider if you can't just place your desired trait modifiers inside the item instead. Also keep in mind that traits, once given, cannot be removed, unless they have a <Duration> which is X turns (strategic/tactical).
To make an equippable item grant you a trait, I would make the item give the unit a battleautocastspell trigger
<GameModifier>
<ModType>Unit</ModType>
<Attribute>BattleAutoCastSpell</Attribute>
<StrVal>Fear_Ability</StrVal>
<Value>100</Value>
</GameModifier>
that spell would then unlock the trait for the unit for the battle. Let me just reiterate that I don't see any reason to do this, because anything you can put in a trait you can put in an item.