While a planted sump will remove a lot of nutrients from the system as a whole, they will not pull them directly from the main tank until the water reaches the sump. The light and nutrients being produced in the main tank will still initially be available to the algae.
The best way to use plants to control algae without completely restructuring the tank is to use floating plants. They'll pull a lot of nutrients from the tank and cover the top which will reduce the amount of light. And they're easy to prune, just scoop out a few net-fulls a week. This might not be an option for you depending on your current set-up, but it's cheaper and more effective than adding a refugium.