It is hard to say. Removing trees that are casting heavy shade on one side of the tree may provide enough light to the tree to allow additional branches to form and start to grow. However, if the tree is large and all of the larger side branches on that side are already dead, then you are left with tiny branches arising from the larger diameter trunk, which can lead to bad branch unions as those side branches age. It is hard for a branch, growing straight out of a large diameter trunk to develop the structure needed to support its weight as it ages, often leading to branch failures. If there are still some of the canopy branches on that side remaining alive, then the chances of a recovery are better. If the dead branches have led to rot or other issues on that side of the tree, then removing the shade will not be that beneficial. Ultimately, some much depends on the condition of the tree, you may want to get a certified arborist out to look at the tree and assess your options.
