Dask implements a large fraction of the pandas API in its dataframes. These operations call the very same pandas function on chunks of your overall dataframe, so you should expect them to be totally compatible.
The resulting computations can be run in any of the available schedulers allowing you to choose whether you are running low-overhead threads or something more complex. The distributed scheduler gives you full control over the split between threads and processes, has more features, and can be scaled out later across a cluster, so is becoming increasingly the preferred option, even for simple single-machine tasks.
Many pandas operations do release the GIL and so will work efficiently with threads. Also, many pandas operations can be easily broken down into parallel chunks - but some cannot and will either be slower (such as joins requiring shuffles), or not work at all (such as multi-indexing). The best way to find out is to give it a try!