Has something similar on the back of my house for a while! I put it there as a very temporary structure when expexting around 30 people for a social gathering, only to find appalling weather forecast for that very weekend. I used sheets of plastic stapled to battens, with more thin battens nailed over them (sandwiching the plastic), and then strips of duct-tape over the top (sandwiching again) to reduce the chance of the threatened wind tearing the thing to shreds before we could use it. We bought some plastic, but as the thing was only ever intended as a one-weekend job, we also recycled the plastic wrappings of a mattress and a wardrobe-type cupboard! Waste not, want not!
After the gathering, in late April, when the lean-to survived not only the weather but also the abuse of numerous guests, it stayed there for the rest of that summer, though the 'front' side came off a few weeks later, leaving the top and ends in place. Opening sections - doors, in effect - replaced the front of the rather hermetically-sealed temporary shell. It then served as a conservatory for the season.
Yes, it did work like a greenhouse / polytunnel. We reared quite a lot of plants in it, and it provided shelter and a warmer microclimate. Irrigation was an issue, as it would be in any covered structure; you HAVE to water, and regularly and often. And temperature was another consideration; hence the opening doors. Skylights would have been better; some way to let the heat out at the hottest point, and encourage through-flow of air. It was too late for me to design in a better solution, unfortunately, and this was one reason why it's not still there. Planning permission might be another, though it was no effort persuading anyone that it was temporary! If you can contrive some opening vents at or near the top, it would be safer; less danger of cooking the produce before it grows! The temperature at the top of our enclosed space was usually above 30 degrees C, and it often peaked above 50 degrees C! I did lose a few plants as a result. Good preparation for Global Warming....
Good luck, John