I don’t think so, see if you want to search for the smallest element, the answer is the root. The second smallest element will be present in the next level, The Third Smallest element should be present anywhere between first 3 levels if not, we couldn’t possible push it up for with 3 operations of remove min element of heap. Since, each element of a level can move up a level 1 time for 1 removal op.
So, to find the Nth smallest should reside in Nlevels. Since, N here is a constant you can search if constant time regardless of the size of heap. Note: we don’t use heap operations here, we do a manual search and the search time doesn’t depend on how big the heap is and heap size doesn’t change the max # of elements present at a level.