Do fallen leaves produce oxygen?
Short answer
It all depends on the time window you are talking about. After having been detached from the mother plant, a leaf will typically keep on photosynthesizing for a few hours or so.

Background
Cutting of the stalk of the leaf results in impaired water flow and wilting. As soon as a leaf is detached from the plant, it will also be cut off from hormones, minerals and other nutrients. The result of this is that senescence (and death) sets in straight away. However, leaves will typically stay green and moist for hours or even days, dependent on the conditions it is stored. Hence, in practice, photosynthesis can be measures at least a few hours after a typical leaf is picked (source: Science and Plants for Schools).