I could not find a report where this has been formally studied but it is highly likely that persons coming to plains after staying at high altitude will feel more energetic, for a few days at least. This is even used by many sports organizations. Quoting from "Human Biological Adaptability: Adapting to High Altitude":
On returning to sea level after successful acclimatization to high
altitude, the body usually has more red blood cells and greater lung
expansion capability than needed. Since this provides athletes in
endurance sports with a competitive advantage, the U.S. maintains an
Olympic training center in the mountains of Colorado. Several other
nations also train their athletes at high altitude for this reason.
However, the physiological changes that result in increased fitness
are short term at low altitude. In a matter of weeks, the body
returns to a normal fitness level.
Following figure accompanies above description:
A number of factors may be responsible for this:
Increased hemoglobin level stimulated by lower oxygen level in air at high altitude
Bartsch & Gibbs (http://circ.ahajournals.org/content/116/19/2191.full) have documented a number of changes in the body that occur on high altitudes exposure from 1 to several days or weeks as in tourists or trekkers. These changes indicate that several systems (especially heart, lungs, muscles and other tissues) are under stress. There are many other reports also documenting these changes. The relief of this stress on returning to plains will give a sense of greater energy and stamina.
The paths in hilly areas are commonly going up and down and it is more exertional than moving around in the plains. Hence, a stay at high altitude often builds exercise capacity. It is like gentle trekking most of the time.
Hilly areas generally have lesser pollution than cities in the plains.
The temeperature and humidity conditions are generally more pleasant in hilly areas.
Psychological factors including relief from anxiety and stress of routine life. It is like one feels rejuvenated after having been on a holiday.
Because of above factors one may feel better stamina, at least for some time, after returning from a sojourn at high altitude.
You may also be interested in my answer on how to avoid acute mountain sickness and its complications (Avoiding acute mountain sickness, high altitude pulmonary & cerebral edema).