Oh, yes, it can be overquilted. If you overquilt, you lose the loft and thus the warmth of the quilt. Not an issue if you want say, a coverlet or a wallhanging. Lots and lots of quilting looks fabulous, but unless you want a summer quilt, you have to do less.
I have seen some very heavily quilted quilts at quilt shows and I can't say that I've ever seen one so quilted that you can't see the pattern of the quilt. Maybe it was the quilter's thread choice rather than the quilting?