It actually is in the FAQ, but it is not directly stated -- "Compensation round picks for Type A and Type B FAs DO NOT qualify for Type D compensation picks."
So this means that the only picks that are not eligible for Type D are Type A and Type B supplemental picks. Please note that with a Type A, you get two picks. The supplemental pick you get is not eligible for Type D. However, the pick that you get from the other team IS eligible for Type D. Also, any Type D is also available for type D. So the answer to your question is yes as long as it is still in rounds 1-3.