As long as your internet connection is active and hasn't dropped then yes the Google Docs will automatically save any data you enter.
But you should always make sure you save the document yourself when you're done working on it to ensure that it saved.
Because sometimes your internet connection may drop and then it won't be able to save your data that you entered so be sure you save the data yourself after you're done working on the Google Docs.
But Google Docs does automatically save your data every few seconds or so in the even that your computer crashes or your power goes out.
I always save the data in Google Docs myself as well though because I want to make sure my important data is saved.