Other than the reserved "handicapped" viewing areas, the stroller-as-wheelchair tag makes not difference at parades. You'll see families with strollers all over the parade route.
If you want to use the reserved viewing areas you'll still need to arrive early; these areas are available on a first-come basis. Please know that it's possible they'll restrict to 1 companion to view from there standing behind the child in the stroller/wheelchair. They cram the
ECVs, wheelchairs, strollers in about elbow-to-elbow. My family actually prefers to stake out our own spot about an hour before the parade, use it as a rest break and have a snack or meal.
Enjoy your vacation!