Weirdly enough, I don't think we are going to see these "neutral runners" get these "neutral" cards for free.
I mean, I guess one of them might. I'm just spitballing here, I think the three "mini-factions" are going to either have their own semi unique card pools, in that they can access certain cards with keywords across all factions, influence free (virus and sabotage cards for instance) or they have some kind of crazy deck building restriction.
Right now, the shards, lucky find and the source are not really condusive to a deck. And yes, this big box will allow you to "fill out" the three mini factions, I cannot really see all of them being influence costing neutral cards. There will be something small for everyone in it.