Fuel consumption is not a binary process. It is not off or on. At any given time of any moment throughout the day your body is relying on different sources of fuel for different energy demands and different organs.
Even if it was, I'd still tell someone that it matters very very little whether you get on a treadmill three times a day for 20 minutes versus one time a day for 60. In the bigger scheme of things, the difference will be completely negligible, and might even favor the shorter bursts. Don't think about what your body is burning for energy. It's just a waste of time. Instead, just use up energy and then focus on what energy you are consuming during the day and what hormones you are manipulating during that energy consumption.
Another thing. Glycogen stores take a long long time to burn through. I think people way over estimate how easy it is to deplete them. But the thing is, depending on your body, that glycogen might purposefully be saved in favor of fat utilization and/or protein use. So again, you might think you've drained it all, but your body started holding onto it for a few different reasons (one is the brain prefers glucose and the brain gets what it wants).
It also matters greatly what level of work you are doing. If you can talk while you're doing it, your body will be able to provide a steady stream of energy through beta-oxidation of fatty acids. If you start working in the range where you are not able to have a conversation you are starting to push yourself into the anaerobic glycolytic pathway, which as the name suggests, means you will need to have some glycogen on hand to use for energy.
But even then, getting caught up in what your body is using at any particular time for energy is missing the overall point. What you should be focused on is the overall amount of energy used period. I'm not going to go into epoc (post exercise oxygen consumption) because it is largely up for debate how important that is. Ultimately what matters is that you are burning as many calories as possible, regardless of the fuel source (and please don't get lost in the "cardio will eat all your muscle away in just three sessions!!!" crowd).
But the first most important thing you should be doing is monitoring what your hormonal signals within your body is doing with the food you are continuing to eat at this time. I'm not talking about androgens here, although they certainly benefit us. I'm talking about insulin and I'm asking it to shut the hell up.
More important than whether you are burning fat in the first 20 minutes of your cardio workout is the idea of what are you doing with the energy coming into your system? What kind of hormonal signals are you sending to your body?
Even a solid cardio workout at best will burn about 300-450 calories, and that can be undone with little effort by not only consuming extra calories, but more importantly, activating your fat storage hormones and telling the body it's time to put away for the "Winter".
So if you're still with me, OP. Do cardio when you can. Do as much as you can do with the time you have. If you are concerned about fat loss and have a lot to lose, concern yourself less with energy utilization and more with energy consumption, and hormonal manipulation. Most of here already know that cardio is great for the heart, it gives us a little edge in the leanness department, but that diet will almost always dictate how we look and feel.
Now go do 20 minutes of cardio and kick some ass.