The energy optimisation performed by the OS is not publicly known.
The exact handling for a particular interface depends on the interface, so some interfaces have very low set up/tear down costs ( e.g. Bluetooth LE), and others are quite cheap to run, but take time to set up and tear down ( e.g. 2G).
You generally have to take a course that gives the OS the best options possible, and then let it do what it can.
We can say a few things. It is unlikely that the connection is being powered up/down for individual packets, so the connection will be powered up when there is data to send, and kept up as long as you're trying to receive. The OS may be able to run at a lower power when it is just waiting, as it doesn't need to ACK packets, but it won't be able to power off completely.
Bottom line, if you send your requests sequentially, I believe that the OS is unlikely to cycle power in between requests, if you send them in parallel, it almost certainly won't.
Is this a worthwhile optimisation? Depends how much of it you're doing.
Possibly of interest: background downloads whereby the OS times your fetch when it knows it is going to do some other network activity anyway.