I think it always happens when a general-meaning word is used in a group of people to refer to a specific thing for too many times, it becomes a Proper Noun, at least within the group. But on the other hand, the original meaning is not lost. The answer to your question should be Yes and No.
Yes, because when you hear the Chinese word "少数民族" without any other modifier or further explanations, it almost always means 55 Chinese ethnic minorities. When talking about the ethnic group in other countries, people tend to use the word "少数族裔" to avoid the usage of "少数民族". For example "华人在美国是少数族裔".
No, because you can always use the original meaning of the word 少数民族. There is nothing wrong with that as long as the background is clear. In this case, you might need modifiers or some other explanation. For example, in fefe's answer "在我们家,汉族是少数民族" will not cause any ambiguity. But if you say "汉族是少数民族" without context, it might confuse most of the people who live in PRC.
PS: Answer is based on PRC experience, and might be wrong or different in other regions.