The preferred_place_id parameter is only used for localizing taxon names to that place (see the documentation at https://api.inaturalist.org/v1/docs/#!/Observations/get_observations_species_counts). You will not get a different number of results if you use preferred_place_id or not, but the common names you see will be the preferred common names for that place.
The place_id parameter will filter results to observations that occur in that place. Depending on the size and type of place and the geoprivacy of the observations, some observations may not appear in search place search results so as to not expose obscured locations. See https://forum.inaturalist.org/t/why-dont-these-observations-show-up-in-this-project-official-topic/12523/16 for a similar issue in the context of collection projects with place filters.
Since you’re filtering your search by project, and the project seems to have a limited geographical range, do you need to filter by place at all? Perhaps you’d prefer simply https://api.inaturalist.org/v1/observations/species_counts?project_id=17900&iconic_taxa[]=Mammalia - Mammal observations in your project not limited by place, and with common names not localized to a place?