This has been done thousands and thousands of times. Each specific case is unique because it will depend upon the gene, the promoter you are using, and the organism in which you express it, so it is not possible to give you a precise answer. But if you have a strongly expressed gene and attach it to a weak promoter, then you would expect in most situations it will have reduced expression. Whereas if you take a weakly expressed gene and attach it to a strong promoter, you would expect it to be over expressed. But there are always exceptions as well.

In multicellular organisms it can even change where the gene is expressed. If the CDS is for a transcription factor then even larger morphological effects can often be observed.