Is it possible to query a node for all addresses containing value? For instance, can I run a query on a bitcoin node, that returns all addresses with more than 1 bitcoin on them?
Bitcoin-core (the full node implementation that makes up the majority of the network) does not keep an index of all addresses and balances, so without writing additional code to do the job, it is not possible. Bitcoin-core keeps track of coins via the UTXO model-- the idea of 'an address with a balance' is just an abstraction of this that makes for a more user-friendly interface.
Of course, you could write some code to create an index of addresses and their respective balances, or perhaps find an already-existing open-source block explorer project that accomplishes this.