Will my Act 3 mercenary's damage benefit at all from having a weapon?

In Diablo 2, giving your mercenary a weapon will vastly increase their effectiveness. Giving my Act II mercenary a 3x socketed pole with Rubies or Topaz for example basically lets them 1-hit everything right up to Duriel.

I've replaced said Pole-wielding mercenary with an Ice Act III mercenary. Reason being that Glacial Spike freezing 3+ enemies is obviously really effective.

This mercenary seems to already do pretty nice damage, but they can still accept a weapon (I think a sword-type weapon and a shield).

I've never seen this particular mercenary ever use a melee attack before (then again, I don't pay much attention).

So, other than having properties that would affect magic damage, resistances or similar obvious benefits; does the weapon help the damage of my mercenary? Maybe it impacts the magic damage even though it would seem odd to do so?

Solution 1:

No, the mercenary's spells' damage is independent of the sword, and the merc rarely uses the sword (I don't recall ever seeing one of them swing his sword, but online sources suggest they do, just rarely, so maybe I just forgot).

It's best to equip them with a weapon that gives other stats, such as resists, faster cast, etc.