No, but there are apps that can do this for you and track not only the time you spend but which app you were using. Can't recommend any, as I've never used them ... but now that I know they exist might check out a few 🙂
Search 'time tracking apps'.
I did find an extension called 'Adobe WorkflowMax' that says it can do this ... but know nothing about it. Note the worflowmax.com website I found says it's compatible with CC 2014. So it may not work anymore or discontinued?
Perhaps others could post if they've used this or something else.