If you want to run a pool, you need access to a node... So yes, they are either running a node, or they are paying somebody to run a node they can query.
The pool needs at very least the header of the previous block, and if they don't want to mine blocks with only the coinbase transaction, they also need information about the broadcasted transactions... And if they want to include these transactions, they need to update their utxo set, so they need to parse the complete blockchain... In other words: they need to run a node