Look at the foundation of the existing shed. Does it have one and is it similar to the house? The screened porch foundation should be tied to the house. How is the shed held together? Is it wood framed with studs or is it made of posts. Now the roof...Is the roof connected to the house? How does the water flow off the shed roof when it rains?
Basically, it's very unlikely that a storage shed will have been built to a standard that is sufficient to convert it to a safe screened porch. Without photos of the existing shed, it's impossible for me to judge that. But ask yourself the previous questions and maybe you can make that judgement.