Can Atala Prism operate or be useful without performing transactions that require ADA?
No. If Atala Prism is going to record its information on the Cardano blockchain (as IOG have said on numerous occasions), then it will have to do so with transactions that pay transaction fees in ADA.
For example, that means that the 5 million Ethiopian high schoolers enrolled in Atala will be driving some transaction volume into the Cardano blockchain.
Some more information you can find on youtube. Atala can store x-thousand DID´s in 1 Cardano-Block. Therefore to create 5 mio ID´s it will not need to creade 5 Mio transactions.
Atala Prism use the public key infrastracture from Cardano.
I think this means that the key to the ID is on the Blockchain but for daily use the ID owner and the institution have not to connect to it because the information is on the users phone and only if the owner make a new degree it will connect to the Blockchain. I am not sure.
Hopefully this will be more clear in future.