Does Eyes of the Rune Keeper allow a Warlock to cast other classes’ spells from Scrolls?

The rules for Spell Scrolls state that:

If the spell is on your class’s spell list, you can read the scroll and cast its spell without providing any material components. Otherwise, the scroll is unintelligible.

However, the description of the warlock’s Eyes of the Rune Keeper eldritch invocation (PHB p. 111) states:

You can read all writing.

Therefore, the writing wouldn’t be unintelligible to the warlock (because the warlock can read it). Thus, if a warlock were to be able to perform any verbal or somatic components for a spell on a spell scroll, could they cast it even if it wasn’t on the warlock spell list?