You can use Airbnb's Sketch to React app to convert your Sketch designs to real React components. There's also a Sketch to HTML app if you need HTML and not React components.
You can drag these components into your React app and play around immediately. Usually people combine that tech with Storybook, so you can browse a live library of your components.
I'd also consider watching for Wordpress and their new Gutenberg release. They're adding React components to Wordpress to replace the classic text editor for posts, so you can drag and drop React components to create pages. This is the easiest way you'll get to "drag and drop" React apps without setting up your own framework/build process.