Um, possibly, but most likely you'll already have their textures and whatnot if you've played multiplayer prior to watching the replay.
"Call yourself alive? I promise you you'll be deafened by dust falling on the furniture,
you'll feel your eyebrows turning to two gashes, and your shoulder blades will ache for want of wings."
Items are apparently downloaded when Toribash starts up, textures when playing multiplayer.
"Call yourself alive? I promise you you'll be deafened by dust falling on the furniture,
you'll feel your eyebrows turning to two gashes, and your shoulder blades will ache for want of wings."