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No it does not

A mountain is a part of spacetime. But it does not "exist" for the mountain.

Certainly the mountain is affected by the environment and can be modelled with the spacetime concepts. But the mountain does not perceive anything, and therefore cannot compute isExist (spacetime)

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I'm willing to call bullshit on this. Space and time may be constructs but they are "helpful" constructs in that they model specific forces which apply to both us and the mountain. I perceive the waste of this body over time: the mountain is subject to these same wastes and transformations as this body.

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