It is likely the power can be used anywhere by the right being.
Each shard has created their own breed on humans in their own image. Ruin and Preservation created mankind on Scadrial, and Honor (Tanavast) also created Mankind on Roshar. Clearly they are working from the same source (wherever they came from before the shattering), but there are subtle difference between the various "humans".
For Scadrians, investiture manifests as the Metallic Arts (Allomancy, Feruchemy, and to a lesser extent Hemalurgy). For Rosharans, investiture manifests as Surgebinding (with Old Magic and Voidbinding being used by non-humans). The difference being the shards themselves.
While every human (seen thus far) has the potential to invest energy, they are limited by the type of power their "god" possesses. Honor can not create humans that can invest Preservation's power, and Ruin/Preservation can not create a being that can invest Honor's power.
In fact, we can see this on a small scale in Mistborn. Ruin can talk to people who are spiked, but can't read their mind. Preservation can read minds, but not speak into them. Their powers remain separate even though they worked together to create beings that can use both.
So to get around to the point here. I believe that any being will always be able to access and use the source of investiture that their creator possesses. For Scadrians, so long as they have metal, they can use the Metallic Arts. For Rosharans, as long as they have storm light and their spren, they can surgebind (this raises the question if spren can leave Roshar, but that's not relevant at the moment).
Hoid is special I think, because he is an original human (not created by any of the Shards) and likely able to use any of the form of investiture if he meets the appropriate prerequisites (consuming the bead of Lerasium)