In General---No. In particular, there are specific factors involving humidity, temperature, and continuous days of use that may make the use of a synthetic bag, easier or safer to use. Condensation between the bivy and the bag may occur. The Alaskan Coast Ranges, for example-- a cold, wet, high humidity climate, year-round---a hard place to keep a bag dry, a down bag (unless you have a means to dry it) will have it's loft degrade over time in such conditions. A synthetic bag which not only will dry out quicker retains most of it's loft when wet. However, in the Sierra, the Rockies, much of the Mountain West, especially in Summer conditions, Down is more than quite acceptable. Of course Down is more efficient than a synthetic bag on a weight to loft basis. It also will have a longer functional life cycle. Synthetic's loft wears out after a handful of years, a Down bag could last 20 years or more.
For myself, in the Cascades and the Sierra in Summer, I use a Tarp, Bivy (water resistant but not proof), Down Bag or Quilt combo. With experience and practice, this can be a very practical, efficient, comfortable, and safe way to go.