Yes, but never in the absence of the Bungie servers. It did have a full sequential single player campaign, but parts of the single player campaign took place in shared instances where the user could see other players running around the map. The single player campaign could also be played cooperatively with other players in the same 'fireteam' if desired, but that was optional.

First, SPC, at least in Destiny 2, required you to do Strikes. Second, you get item drops. Technically there is no SPC in either Destiny because it's an MMORPG. There are just plenty of things you can do all by yourself and things that you meant to do alone, and those things usually come with item farming, so you need server-side to make it fair.