One way to approach the problem is to ask, If this is not the way to get silence at a distance, what is? The answer, I would think, is the Imbue arrow ability of the Arcane archer. If the OP's idea works, then Imbue arrow becomes useless, doesn't it? That would suggest the plan doesn't work...
RAW would perhaps suggest an arrow is ineffective, but I'd be tempted to allow it cast on a small object that gets lobbed to the square the enemy spellcaster (or whatever) is in. A one-round action would allow the ES to kick it away (having made a successful spellcraft check?) and the action has an effect on combat (allowing the players to be rewarded) but not a game-breaking one.
My 2cp.
RAW would perhaps suggest an arrow is ineffective, but I'd be tempted to allow it cast on a small object that gets lobbed to the square the enemy spellcaster (or whatever) is in. A one-round action would allow the ES to kick it away (having made a successful spellcraft check?) and the action has an effect on combat (allowing the players to be rewarded) but not a game-breaking one.
My 2cp.