That will work fine so long as you are in a sub-tropical area. If you get below 50 F during the winter months, you would need some way to enclose that area. That is, unless you are growing cool-loving orchids, those that can handle temperatures into the 40's.
I have a large screened in patio, but there is a roof, not a pergola. In November I enclose that porch with clear, marine vinyl panels (4' x 6') and then heat that space. There are six panels total plus a 2' x 5' panel above the double-doors. Next fall I want to cover those panels with Solar Blanket material, to give it much better insulation value. I haven't figured out how I am going to do that, since I want to roll up the "bubble-wrap" panels when the weather is nice so that we can see out of the porch.
