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 colorfastness). It is our understanding that burning the plant is the only way the oils can be airborne.