I think it would work great and I do something similar. There are overstory trees with more skeletal, open canopies like Mamey Sapote, Guava, and some Avocados that will let through lots of light. Especially when those trees are young you have essentially full sunlight. It's much easier to grow vegetables in partial shade.
Just make sure that whatever you plant very close to the trunk isn't a root crop that you have to dig down to harvest. Sweet potatoes, ginger, turmeric, etc are all bad ideas to intermingle with the central root ball.
I have had good results with Mavuno Cow Pea, Bush Long Bean, Eggplant, Lolot Pepper Leaf, Longevity Spinach, Sissoo Spinach, Okinawa Spinach, Pineapples, Lemongrass, Garlic Chive, Ground Cherries, Everglades Tomato, and some squashes and pumpkins. You can plant any of those pretty close in to the trunk. A few feet further out go with Turmeric, Ginger, Galangal, Cardamom, Sweet Potatoes, Cassava, Taro Root or whatever other root crops you're into. Canna Lilies and Heliconia are also great but they spread by rhizome so keep them a safe distance from the tree roots.