Yes.
Rulebook:
"When you draw a card from the box, unless you are told to draw a specific card, draw a random card of the appropriate type by shuffling the cards you’re drawing from and drawing the top card.
This applies to actions other than drawing.."
Which is then corroborated in the example (Simoun's turn) by the scorched ruin summon and acquire close, which summons a random weapon from the box.