As far as I know, being part of a gifted program has zero influence on college and BA/MD/DO admissions.
Admission officers will consider the rigor and content of classes, but simply being part of a program for gifted children has no influence on admissions.
For admission purposes, a student’s GPA will be recalculated to remove any weighting (extra GPA points) a school has placed on more difficult or advanced classes. Admission only considers the unweighted GPA. This is also true for med school admissions.