Yes. Ketostix just indicate the presence of ketones, not if it's body fat or dietary fat being used. It doesn't matter the source, though--if you're eating less than you need, your body will have to tap into bodyfat as well.

Also, the stix only indicate ketones that have spilled over into the urine. Ketones build up in the blood first, and then are used...for a lot of low carbers, after a few weeks their bodies get efficient at using ketones and they won't have spillover into the urine, at least, not at a keto-stix detectable amount.

Actually, it's not the high fat that will induce ketosis, but rather the low carb. You can do a low fat, low carb diet and easily be in ketosis.

Fuel Sources during exercise:
*Muscle glycogen is the primary source of CHO during high intensity exercise, and supplies much of the first hour of exercise.
* Blood glucose is converted to glycogen via the liver during gluconeogenesis and is important during low intensity long duration exercise.
* Intramuscular triglycerides are the primary source of fat during higher intensity exercise.
* Plasma FFA are converted to acetyl co-a and enters the Krebs cycle, and is the main source of fat during low intensity exercise.

What this means...
During low intensity exercise (approx. 20% VO2 max) there is an increased energy expenditure (approx 60%) from fat, however the total expenditure of energy and fat oxidation is low because of the low intensity.Theoretically it would make sense that because there is an increased energy expenditure you would use more fat during low intensity exercise, however it would take a long time to expend the amount of calories needed to lose weight. At higher intensities (approx. 50-60% VO2 max) there is a lower % energy (40% from fat), however the total energy expenditure and fat oxidation is higher. Therefore, a combination of high intensity & duration (intervals) has proven the most effective way to lose weight.