No, I think you've severely misunderstood what is going on here.
First and foremost: Bitcoin is completely dependent on the availability of lots of power (for proof-of-work calculations) and network connectivity (to distribute unmined transactions). Without both of these, it cannot operate. Adding satellite transmissions to the picture doesn't change this. In any sort of apocalyptic scenario like what you're imagining, cryptocurrency will be one of the first technologies to become unusable.
Additionally, all that's going on here is that a company is using several commercial satellites to transmit the blockchain, as well as some user-specified data. These satellites do not belong to Blockstream, and are not controlled directly by Blockstream's clients.
First and foremost: Bitcoin is completely dependent on the availability of lots of power (for proof-of-work calculations) and network connectivity (to distribute unmined transactions). Without both of these, it cannot operate. Adding satellite transmissions to the picture doesn't change this. In any sort of apocalyptic scenario like what you're imagining, cryptocurrency will be one of the first technologies to become unusable.
Additionally, all that's going on here is that a company is using several commercial satellites to transmit the blockchain, as well as some user-specified data. These satellites do not belong to Blockstream, and are not controlled directly by Blockstream's clients.