Low intensity exercise can be beneficial in some circumstances in this situation of pre breakfast excerise but not for all exercise. Why? Cos your insulin will be lower and your body will oxidise more fat BUT only at lower-moderate intensity (walking, low impact stuff not running or weights). Oddly tea/coffee can actually help this process (but not too much that is counterproductve is stimulates epiphrenene a hormone and that can lead to cortisol release - the naughty hormone as it can increase fat gains).
I have porrige made with water, add some blueberries then I pour on a fat free yoghrt and can train an hour later with no noticable effects.
Obviously if you have health issues, diabetes this is non starter. But go with a cup of green tea, tea or coffee then exercise low-moderate and should be all good.