It seems from the din of making succos under trees that the problem is that the sechach needs to do the shading and not other trees. Can one therefore use a clear shlock or cover for the succah? The sechach will therefore do all the shading still?
It is true that in discussing sechach pasul, the Gemara and the Poskim refer to issues of shade and sunlight (if the kosher sechach provides sufficient shade without requiring the non-kosher sechach, the succah is valid). Based on this, the Shevet Halevi (4:57) cites from somebody who suggested that there is no problem of covering the sechach with a nylon see-through sheet.
However, the Rosh (cited by the Beis Yosef 631) writes that sechach protects from the sun and the rain, and Rav Wosner proves from here that even a plastic sheet that means to protect from rainfall is considered a layer of sechach pasul.
His conclusion is therefore that a plastic sheet is certainly sechach pasul, and the status of the succah will depend on the two opinions mentioned in the Shulchan Aruch (629) concerning a kosher succah with a protective sheet. On account of the safek one should therefore sit in the succah, without reciting a berachah.
See also Har Tzvi, Succah 22, who also discusses the issue.