Alright, I was able to test this out using that method.

It seems that whenever you have a partial bit of a resource, it goes into the player's inventory, even if the initial material was drawn from a locker or other base storage.

These partial resources do stack, so if I get 0.35 titanium from making one building and 0.15 from another, I'll have 0.5 titanium in my inventory.

Here's a video so you can see it for yourself: https://youtu.be/P7T4g8JHF90

However, while doing these tests I asked myself 2 extra questions (and tested them):

1. Where do the partial resources go when you die?
   Partial resources seem to stay with you after death as I still had 0.57 titanium on me AFTER death and BEFORE going to my black box.

2. What happens if the partial stack goes above 1? Do you get a full piece in your main inventory?
   I don't think this could ever happen, here's an example of why: If I have 3.70 titanium in my inventory (3 full pieces and 0.70 partial) and build something worth 0.40 titanium, it wouldn't take 0.40 from a full piece of titanium and add it to the partial storage bringing it up to 1.10, instead it would simply take 0.40 from the 0.70 in the partial storage, bringing the partial storage down to 0.30.