Additionally, if so, what strategic advantages would capturing a largely empty town provide? And where would those living in that town tend to go?
Totally deserted in very few cases, but a towns population would naturally fluctuate quite a lot in relation to the events of the war, like an approaching frontline or strategic bombing. A good example of this is Hamburg, the 2nd biggest German city after Berlin. Hamburg was the target of a devastating series of bombings (in fact, the most devastating attack of this kind in Germany) between 25.7.1943 and 3.8.1943, aptly named Operation Gomorrha. The concurrent raids caused a firestorm that in the end killed 34.000, wounded 125.000 and robbed 900.000 of their home. Worse, the infrastructure, with the exception of waterways and the important harbour, had totally collapsed, there was no gas, no water and no electricity in parts of the city. This led to a mass exodus of almost a million people until 8th August, most of them put into provisorial camps in surrounding rural Schleswig-Holstein and Niedersachsen, transported by army and civilian lorries, train (the stations at Altona and Bergedorf, in the western and eastern parts respectively, were still operable) and ship down the river Elbe. The supply situation for all of this refugees was pretty dire in the beginning, and this led to a lot of resentment towards the authorities who were at first totally overwhelmed with the problem. Many of the refugees couldn't stay in the overfilled reception areas outside of Hamburg and were sent to distant areas of Germany or the occupied territories, and the people they were quartered with often met this imposed cohabitation with little patience or benevolence. The turn to your original question is that if one town is deserted, another has to become overcrowded.
As a result of the difficult conditions for refugees, many returned already in August and September of 1943. It's difficult to give exact numbers, but based on the number of food stamps given out, a rough picture of the fluctuation of Hamburg's population can be given:
The total destruction of several city districts led to a lot of internal changes, though, and many of these districts were closed off (because of the danger of disease outbreaks and collapsing buildings) and stayed largely empty until after the war. Hammerbrook, f.e., with 27.440 inhabitants had just 66 after the bombings. The destruction of over 250.000 flats meant that many of the returning people had to find alternative living spaces. One possibility were bowers (home for ~200.000 during that time), or using the still intact cellars as homes.
In total, the population of Hamburg changed from 1.698.388 to 1.406.158 between May 1939 and Octobre 1949. Heavily hit districts such as Hammerbrook, Hamm, Rothenburgsort or Barmbek still only had as little as 2-15% of their pre-war population in 1949.
A problem for many German cities, particularly towards the end of the war, was that authorities actively tried to hinder relocation by their citizens or stall active evacuation. Berlin still had about 2,7 million people living there at the beginning of the battle of Berlin (compared to 4,3 million before the war, a number that hasn't been reached again today).
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