When placing a block connected to any fences (not fence gates), the placing sound to any block will not play, including another fence, as long as the hitbox will surround the fence, so it'll still play if touching if placed on a different nearby block. When placing something like an item frame, the sound will however play as it's an entity.

This image shows when placing a block on a fence, the sound will not play; as prove the subtitle will not show. As prove subtitles are on, there is lava pops and block breaking to show the subtitles are on.