Making piglins drop arrows on death if they are holding a crossbow

Would this work?
  "type": "minecraft:entity",
  "pools": [
    {
      "bonus_rolls": 0,
      "entries": [
        {
          "type": "minecraft:item",
          "functions": [
            {
              "count": {
                "type": "minecraft:uniform",
                "max": 2,
                "min": 0
              },
              "function": "minecraft:set_count"
            },
            {
              "count": {
                "type": "minecraft:uniform",
                "max": 1,
                "min": 0
              },
              "enchantment": "minecraft:looting",
              "function": "minecraft:enchanted_count_increase"
            }
          ],
          "name": "minecraft:arrow",
          "conditions": [
            {
              "condition": "minecraft:entity_properties",
              "entity": "this",
              "predicate": {
                "equipment": {
                  "mainhand": {
                    "items": "minecraft:crossbow"
                  }
                }
              }
            }
          ]
        }
      ],
      "rolls": 1
    }
  ],
  "random_sequence": "minecraft:entities/pigin"
}```