I don’t think that would happen. Currently, Starlight runs on all non-party nights during the MNSSHP season. I think that would hold true during MVMCP.
Seeing the Christmas parade at night is only during the MVMCP, and once the parties are done, it replaces the daytime parade until about Jan 1.
Just to set people at ease, I found where WDW stated this.
" Please note that the parade will not be available on evenings Magic Kingdom hosts Mickey’s Very Merry Christmas Party, but the parade will continue throughout the holiday season — after all, the cold never bothered us anyway."