Can an Evocation Wizard that casts Wish to duplicate Chaos Bolt add their Intelligence modifier to the damage?

Question

The Evocation Wizard gets the Empowered Evocation feature which states:

Beginning at 10th level, you can add your Intelligence modifier to one damage roll of any wizard evocation spell you cast.

The wish spell states:

The basic use of this spell is to duplicate any other spell of 8th level or lower. You don't need to meet any requirements in that spell, including costly components. The spell simply takes effect...

Notably, Empowered Evocation only applies when you cast wizard spells, but the chaos bolt spell (XGtE, p. 151) is sorcerer-exclusive.

And there are features which explicitly say that the spells that are not normally considered part of your class now are, such as the Arcana Cleric's Arcane Initiate (SCAG, p. 125), which states:

When you choose this domain at 1st level, you gain proficiency in the Arcana skill, and you gain two cantrips of your choice from the wizard spell list. For you, these cantrips count as cleric cantrips.

However, the wish spell has no such clause.

To avoid an argument about whether you even cast spells duplicated by wish I would like answers to assume that duplicating a spell using wish counts as casting the duplicated spell.

What I am still unsure of is: If a Wizard duplicates a spell with wish, does that spell now count as a Wizard spell?

Answer 1

No, because Chaos Bolt is not a wizard spell.

While I might not agree with it, you told us to assume you cast spells duplicated by wish, so I will.

Empowered Evocation says you can add your Intelligence modifier to one damage roll of any wizard evocation spell you cast. Chaos Bolt is not a wizard evocation spell because it does not appear on the wizard spell list.

Answer 2

No, because duplicating a spell with wish does not count as casting it.

You ask us to assume that duplicating the spell does count as casting it, but since the evidence doesn't support that conclusion, the evidence also doesn't support anything predicated on that conclusion. As Abraham Lincoln said:

Q: If you call a tail a leg, how many legs does a dog have?

A: Four. A tail still isn't a leg.

Wish causes the spell to take effect. It does not cause you to cast the spell. (This is different from magic items that say "you can use an action to cast magic missile" or something to that effect.)

You aren't meeting any of the requirements to cast the spell: you don't perform its components, spend the full casting time concentrating, or expend a spell slot. You don't even have to know the spell. Because you aren't casting it, class features that modify casting a spell (most importantly metamagic, but also the Evoker damage boost) don't apply.