It would obviously benefit the player, but less likely the Celtics. Neither Hunter nor Young make the minimum, so they are less likely to be claimed by another team off waivers (since a team would need cap room, which is not the case for minimum-salary players.)
Additionally, if the cut player did not find an immediate NBA home and chose to go to the D-league, Portland could get first dibs if said player is one of the Celtics final three cuts. Accordingly, they could remain in Boston's system in case it made sense to re-sign him to a contract later in the season (if injury or a trade caused such a maneuver to make sense). If said player were re-signed later in the season without signing with a different NBA team first, the Celtics could even maintain Bird rights.