Can humidity spread poison ivy oil?

Most likely, no. However, if any of the leaves have fallen onto the deck/chairs in previous seasons, the oil may be on those items, leading to secondary contamination. That would be the most likely cause for a person to develop a rash in this case. If so, you may consider wiping down the furniture with Tecnu (after spot checking first for color-fastness). It is our understanding that burning the plant is the only way the oils can be airborne.