Charlotte,
That's a yes and no question. It does make a difference if you can't push as hard on a empty stomach. If you can't then you don't burn as much. If you can then you'll burn the same. There has been quite a few studies done with workout out on an empty stomach and for some people it does toss them into starvation mode during and a little bit after a workout. As they haven't had food for at least 8 hours, usually a bit longer then the 8 hours, as most of us don't eat right before bed. So your looking usually at a good 10 hours or a bit more of no food and then you decide to jump around and do all this activity, on top of not having food for 10 hours +. Something you'd never do, if you were awake all day. How may times have you decided to workout 10 hours after breakfast with no snacks or other meals in between? Just is a no go, for any of us who workout out hard. But we'll do it after sleeping, the night away. And this is the reason why some people go into starvation mode when they do this, it's just too many hours without food and 0 fuel, for them.
There as also been quite a few studies done about this, and on a 75% average you lose weight better if you eat before working out then not eating. But there's also that 25% in there, that for some reason it didn't matter if they ate or not.
HTH,
Kit