Would it be possible to have a NPC guild or faction for story purposes, but not actually have a guild set up? Like a mining guild or something for my alt to control?

It's safe to say that throughout Arda there are many different organizations and factions. So, it's safe to assume there would be one out there specific to the purpose you are looking for. However, I don't know if you would be able to say you controlled this guild unless you had the intention of starting it.

Personally, I had the Marauders act as an NPC group for a long time before making them, but in the end I did make them. So, Im not one hundred percent sure. But I'm positive Loth or someone could answer the questions a bit better than I could.

Stick to only participating in the guild, not saying that you are in charge of it. Otherwise you need to be working on actually starting said guild.