I use serger thread for piecing and normal sewing all the time - it's only two-ply, so it is not as strong as a 3-ply thread.
In quilting, the stitches are a little more likely to break than stitches made with 3-ply thread, especially in areas that are not heavily quilted.
I haven't noticed this problem with it in quilts that are quilted closely - 1-2" apart.
Serger thread is usually polyester and some people don't like putting poly in their quilts - personally, I use poly or cotton, depending upon the color, weight and effect that I want.