I have done that in the past and did not get a good kill. I really think it depends on how high the grass/weeds are that you are mowing. My problem was the clippings were so thick that I did not get good contact with the herbicide.
I did it on my LC mix plots this summer. As others have said, it's best to wait for regrowth to get a more effective kill, but you can definitely get the job done by doing it on the same day. Especially if your goal is mainly a fall hunting plot. You'll have better luck if the existing growth isn't too thick. Good luck!
In my experience, it's not optimum, but sometimes you have to do what you have to do. I agree that you can get away with it now much better than in the spring. Some vegetation has about ran it's course for the year now. I mowed a few plots early this week and sprayed them Thursday. Had quite a bit of thatch so I'll soon see, but I have done it before and been successful. Good luck !
On another property I hunt, I sprayed gly today. I mowed it about a month ago thinking it's August, so it ain't gonna grow much more. Wrong ! We had ten inches of rain in August so I upped my gly ratio a little to put the hurt on the the rathere tall grass and weeds in the plot. I'm leaving Friday for speed goats in Wyoming, hope it's dead when I get back.