I have done other fitness activities on an empty stomach. It resulted in me dry heaving after one point. I personally do not recommend it based on experience. Starving yourself is not how you lose weight...
...Well, I came across some research that suggests *IF YOUR GOAL IS WEIGHT LOSS* (as opposed to fitness), you should eat *AFTER* training if you are male and *BEFORE* training if you are female. That is, simply shifting mealtimes rather than starving or skipping meals completely. There ws no reason given, just that they monitored and surveyed amateur athletes and that was the result.
Whenever I've looked at weight loss studies in detail, the gains in loss are always utterly marginal. As in say "the average loss was 1kg but for those who ate after they trained the loss was 1.02kg. In my book, as long as you consume less than you use, overall, and measured over weeks/months, rather than days/hours - you'll lose weight. You might even get weird sh*t happening: like after a few weeks of nothing happening, you lose heart and go on a bit of a burger and chocolate spree for a few weeks, and that's the point at which you start losing weight! It doesn't mean you can carry on like that forever, there comes a point where it reverses. As long as, over say 4+ months, you go to bed at night with a slight calorie deficit - you'll lose weight.
In my experience (using the ergo as the measuring device) you need to lose double what the exercise machine tells you you've lost. So a 2000 calorie workout on the ergo, equates to a 1,000 calorie workout in reality.