Can I revive a negated monster this way?

Lets say my Thought Ruler Archfiend gets negated by solemn warning. If I remove it from play with Silent Psychic Wizard's eff will Thought Ruler be brought back when Wizard leaves the field?

No, a Synchro monster whose summon was negated cannot be re-summoned in any way.

Synchro Monsters, Xyz Monsters, Fusion Monsters, and Ritual Monsters are all considered "Special Summon Only" monsters similar to BLSEOTB. They have to be Special Summoned properly and successfully before they can be re-summoned unless they are returned to the deck/extra deck.