Yes. What actually happened is that the chronic Carb based pattern caused resistive states of the “Fed State” anorexigenic hormones like insulin and leptin. This enabled fat gain. Eating a fat based, lipolytic pattern reduces and eventually eliminates this resistance. The goal is to get to a balanced, insulin-glucagon and leptin-ghrelin secretion state when you can consume either fat or carbs with equal efficiency. Overall detrimental effects of a chronic, Carb based pattern are dealt with at the same time.
If you’ve been eating primarily lipolytic for two months, you can experiment. It’s highly unlikely that you consumed enough carbs to halt the adaptive process, you just temporarily suspended lipolysis. Now, this is not a requirement, just an option, especially if you’re experiencing energy balance issues possibly indicating negative metabolic effects. This varies widely for individuals according to multiple factors. However, it’s also OK to just take a short break and consume some foods you’ve missed. No big deal. But, you may find that some now affect you in not only different, but distinctly unpleasant ways…