Could you specify what you mean by "surrendering"? The Wehrmacht surrendered as a whole. Do you mean if soldiers returned home without being POWs first?
To expand on OP's question, did this vary significantly based on where the German soldiers were?
As for the first part of the question: Yes, that did happen and is often memorialized in family memories around Germany and Austria. Mostly in the form of people who either got cut off from their units and just went home because they saw the war was over or in form of people actually actively trying to ditch their clothing and weapons and just pretend to be civilians.
The reason we can reconstruct this phenomenon is because sometimes it didn't work and that had terrible consequences for those attempting to do in form of the Wehrmacht's military justice. The Wehrmacht military justice system in all its criminal nature did continue to operate all throughout May 1945 and even beyond May 8/9 and the official unconditional surrender of all German forces that marked the end of WWII.
The Austrian Documentation Center for Resistance published a special volume on resistance in the army and was able to find documents that show that on May 9th, 1945 the military court of the 6th Mountain Division sentenced 15 soldiers of Austrian origin who had gotten rid of their uniforms and begged for civilian clothes from a nearby farmer to death. A sentence they carried out the same day despite the war having officially ended. Similarly on May 10, another military court in Austrian executed another four death sentences on the spot against people they had taken into custody three days before after they had left their units and tried to return to their homes not far away.
Even in Allied POWs camps, Wehrmacht military courts continued to operate and do so in a fashion that was clearly criminal against alleged deserted who in the end days of the war had decided they were to leave their units but were picked up by Allied troops, or had handed over the towns they were defending to the Allies or other alleged crimes.
The mos notorious of these cases is that of Hans Filbinger who was a German Navy Judge with troops in Germany and Norway and from 1966 until 1978 president of the federal German state of Baden-Württemberg of the CDU party. In the so-called Filbinger affair, it emerged that as a judge, not only had he presided over "ideological" trials such as sentencing soldiers who had expressed a distaste for Nazism to death during the war, he also had sentenced someone who had considered deserting but had not actually done so in January 1945 in Norway and also sentenced a man named Kurt Olaf Petzold to six months in jail as part of a still operating Wehrmach military court in a POW camp on May 1945. Petzhold had been indicted for because during his internment as a POW he had told his commanding officer that said officer was a "Nazi Dog".
The problem is that there was such a slew of "Schnellverfahren" (expedited trials) against those Wehrmacht soldiers who tried to go home when the war was clearly lost and who were sentenced to death usually, that we actually don't know how many of them actually died in the last weeks and days of the war and even beyond the unconditional surrender. Many of these trials remained undocumented because they literally consisted of just one officer or jurist preceding over it and sentencing people to death, despite the situation of the Wehrmacht in May 1945 making it understandable that people just wanted to return to their families rather than spend time as a POW or similar.
Despite the fact that this was a clear injustice of the Nazi system, the victims of Nazi military justice who survived these trials were only rehabilitated in Germany in 1997 and 2002 respectively and in Austria in 2005, meaning that before these dates, former Wehrmacht soldiers who at various points in the war had either tried to desert or resisted against the Nazi system otherwise or who were e.g. sentenced for homosexuality had previously lived with a criminal conviction in their record.
The reason this took so long was a resistance by conservative and right-wing parties – mainly those who had previously been at the forefront of popularizing the "clean Wehrmacht" myth and granting a wave of pardons and amnesties to all Nazi criminals convicted by the Allies in 1955 – against granting rehabilitation to people they viewed as deserters and therefore criminals. So, in the eyes of the German and Austrian justice system, people who had left the Wehrmacht either because of their opposition to the various criminal activities of the army or who had just wanted to return home in 1945 because the war was lost were criminals while people who had carried out mass shootings were actually granted amnesty if they were convicted at all.
As for the Allies looking for them: The occupation authorities were very keen on privately owned fire arms as well as finding Nazi criminals but regular former soldiers who would have been processed as POWs not so much. Because of the issues of logistics and actually feeding and processing all these people in a variety of ways, the process for POWs in the zones occupied by the Western Allies was actually rather quick so that resources and effort could be focused on the 15 million Displaced Persons, meaning refugees, former forced laborers and Germans driven out of various territories rather than the POWs. So, in the Western Zones this all went by comparatively quick. The Soviet Union is a different matter though they mostly focused on German POWs they had captured during the war and the last ones of whom were released in 1955.
So, there were no coordinated searches for former Wehrmacht members though if one of them came in contact with the Allied occupational authorities – as tends to happen during an occupation, especially with denazification going on – they would have been picked up and screened and processed, at least initially.
After all though, while we don't know the exact number of those who managed to get home as well as of those who were caught in the military justice system, the percentage of those measured against the number of men serving in the Wehrmacht was rather small by all indications. Mainly because until the very end, the Wehrmacht remained an ideologically indoctrinated fighting force of Nazism.
Sources:
Ian Kershaw: The End. Germany in 1945.
Wolfram Wette (Hrsg.): Filbinger, eine deutsche Karriere.
Dokumentationsarchiv des Österreichischen Widerstandes (ed.): Schwerpunkt: Bewaffneter Widerstand - Widerstand im Militär.
Georg Auer: Die Spruchtätigkeit der NS-Militärjustiz und die Vollstreckung wehrmachtgerichtlicher Todesurteile in Hamburg.
Manfred Messerschmidt, Fritz Wüllner: Die Wehrmachtjustiz im Dienste des Nationalsozialismus. Zerstörung einer Legende.
Richard Bessel: Germany 1945: from war to peace.
Edit: Clarified a sentence.
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