No, "laying claim" to mineral deposits not on Earth is valueless. Even if, in a rather fanciful world, said claim was in some way legally enforceable.
"Having technology able to recover said deposits and deliver them to an area of meaningful economic activity without costing several multiples of the value (or, more realistically, several thousand multiples of the value) of the minerals in question" would certainly justify a very high valuation for SpaceX. But they do not have such technology, and it is far from clear that they are on the path to having that technology anytime soon.
And nothing has much present value today based on its prospective value in centuries. In 100 years, we could be superintelligent nanotech swarms. Or extinct. Or anything in between. Only a fool would place much certainty on the value of a mineral deposit that far out.
I imagine it would be difficult for earth-based entities to enforce jurisdiction in far space. If you already have possession of an asteroid, it doesn't seem like there's much terrestrial governments could do shy of import tariffs. And whomever holds to material has one massive advantage in terms of MAD: they're sitting high up in the gravity well.
Certainly SpaceX has an air of "tool builders" about them -- they'll build the shovels and pick axes of the space economy. As evidenced by their current economic successes, they're banking on the evolution of the industry -- not a quantum leap 100 years hence.
A great (related) scifi novel: The Moon is a Harsh Mistress by Heinlein
"Having technology able to recover said deposits and deliver them to an area of meaningful economic activity without costing several multiples of the value (or, more realistically, several thousand multiples of the value) of the minerals in question" would certainly justify a very high valuation for SpaceX. But they do not have such technology, and it is far from clear that they are on the path to having that technology anytime soon.
And nothing has much present value today based on its prospective value in centuries. In 100 years, we could be superintelligent nanotech swarms. Or extinct. Or anything in between. Only a fool would place much certainty on the value of a mineral deposit that far out.