Yes, it is possible. I personally think the night scenery of the Bird's Nest and Water Cube is more beautiful.
After visiting Badaling, you will go back to Beijing by train or bus. If by train, you may walk to Xizhimen to take Beijing Subway(https://www.travelchinaguide.com/cityguides/beijing/transportation/subway.htm) to Olympic Park station. If by bus, you may walk to Jishuitan subway station from Deshengmen to take subway to the site. Transfers between subway lines are needed. Good luck~