Can a Trickery Cleric cast spells through their duplicate when the Cleric would normally be unable to cast spells?

Inspired by this question, can a Trickery Domain Cleric get around effects that would normally prevent the Cleric from casting if they move their Invoked Duplicate outside of the effect?

As a concrete example; the Cleric (Bob) gets into a battle with another spell caster (Daryl). Daryl wants to keep Bob at bay and casts Silence trapping Bob in a soundproof area. Daryl invokes his duplicate (no sound required) and has the duplicate run out of the range of the Silence spell to attack Daryl.

So with Bob in the radius of a Silence spell, can he cast spells via his duplicate that is outside of the spell effect?

Per the spell description:

For the duration, you can cast spells as though you were in the illusion’s space, but you must use your own senses.

So Bob casts as if he was in the illusion’s space, not effected by Silence. And “talking” isn’t a “sense” like vision or hearing. So that should not be an issue.

Can Bob hit Daryl with an Inflict Wounds to try and break Daryl’s concentration and lower the Silence spell?