That will probably work about as well as the proposal to put a data center on Sealand [1]. Or Cryptoland. Or Satoshi Island. Or Blueseed.[2]
Or the Space Kingdom of Asgardia, which launched a successful satellite with some data storage in 2017.[3] That lasted until 2022, when the satellite re-entered.
[1] https://en.wikipedia.org/wiki/Principality_of_Sealand
The people who originally sent the thing up, can give up their access.
As long as you don't have to physically touch the thing again, you can use some clever cryptography, so that no one is technically running it.
That's easiest, if you just let no one have any privileged access. But you can use (public key) cryptography or similar to give some anonymous people on earth access. Or, for peek publicity value, the data centre can give access to whoever holds a specific bitcoin.