The answer to this question is very case specific.
In general, if you register a combined mark, all of the dominant elements of the mark gain implicit protection. If a third party copies one of the dominant elements of your trademark, you would be protected.
However, the element must be distinct enough to gain protection when used separately. If the copied part of the mark is generic, the protection doesn't apply. In such cases, for the protection to apply, the mark would have to be copied fully.