Tarlach, that happens only in the liver or kidney.
During a workout, it is true that you are undergoing gluconeogenesis and lipolysis at the same time. However, most of the fat you're burning is stored outside of the liver. During a workout, the majority of the glycerol formed from the breakdown of fat outside the liver doesn't enter gluconeogenesis. Instead it is taken up by muscle (or other) cells, converted to acetyl CoA, and finally enters the Krebs cycle.
In animal models, even in a fasted (partial glycogen depleted) state the liver can only take up about 25% of the glycerol found in the bloodstream. The rest is utilized by other body tissues. Again in animal models, inhibition of lipolysis does not significantly change the rate of glycogen depletion. The conclusion that can be drawn from this is that the products of lipolysis are not major players in synthesis of glucose for glycogen repletion.
I'll concede that it is biochemically possible. But let's talk about reality. The contribution of triglyceride metabolism to glycogen repletion is small compared to the others I listed (dietary carb, dietary protein, and protein catabolism).
Fat -> glucose -> glycogen just isn't a significant part of our metabolism.