Does "Quality Joe" affect the drop rates of turds?

In the game you need a lot of turds, in order to make Fertilizer. However, the toilets drop them very rarely. Does the perk Quality Joe or any other Perk affect the drop rate of turds?

According to the Wiki page you have linked:

Quality Joe has 3 ranks that raise the general quality (but not rarity) of items found when scavenging.

A common misconception about Quality Joe is that it increases your chance of finding rare items. The thought is that maxing out the perk could make the difference between finding Paper and finding a rare schematic or weapon. This is not the case. Quality Joe only improves the quality level of items found.

Quality Joe doesn't increase the chances of finding an item, just the quality of an item. From what I can find, I don't see any perks or skills that increase the chances of finding items, just thing's that impact loot time and quality.