Army betrayals absolutely had an effect. Probably not a large enough effect that it changed the outcome of the war, but it could definitely be argued that it shortened it. Hitler became very distrustful of the Army after the attempt on his life by Army officers. At the begining of the war, one of Germany's major strengths was that commanders usually had licence to make decisions on the fly - they were given goals, and it was up to them how to achieve them. This naturally allowed for more fluid opportunistic decision making in the field. After the attempt on his life however, Hitler ran the ship. This led to less decision making from the Army and major decisions coming down from Hitler himself. With regard to the Battle of the Bulge (as per the documentary below) the few commanders that were able to make tactical decisions were sometimes too scared to act on fear of angering Hitler. This had a large effect on the German army's ability to perform in the field.

Source: 32:15 of https://youtu.be/AJitx9YgZjE