I have not found any evidence that engorgement affects the milk ducts.

Engorgement may affect the secretory cells that develop on the basement
membranes, therefore affecting lactation for that cycle. But since the ducts
develop during puberty and pregnancy, it is unlikely that they are affected
by engorgement.

Linda J. Smith, BSE, FACCE, IBCLC
Bright Future Lactation Resource Centre
Dayton, OH USA
http://www.bflrc.com