That's correct and it's most likely due to the chemical nature of those processes. Dopamine is not just a neurotransmitter but it is also the chemical precursor of adrenaline which gives you the feeling of being energetic or excited about something. So the OPs advice of accomplishing a task first thing will actually increase your mental and physical energy if it provides you with a reward. What you say is also correct because we can exhaust our capacity to perform mental work just like we can with physical work. I think the point in the article still stands though, it's almost always the case that you can trigger a burst of mental energy before you have started working on something even if you feel tired. If you've already been working on something for quite some time then your chances of triggering that burst of new energy are much lower and it might be wiser to take a break and come back to it fresh.