In other words, if I have less than 1.5TB to play with, is --no-ancient-blocks essential?
with or without warp, unless you are running
--pruning archive you should only be using around 150gb at the moment. (https://wiki.parity.io/FAQ#what-are-the-parity-ethereum-disk-space-needs-and-overall-hardware-requirements) Regardless of whether or not you warp sync, you download all blocks from genesis.
A common misunderstanding however, is that blocks contain state information, and you require every state since genesis to have a full node. Blocks only contain transactions which act on the state. An archive node (the 1.5TB you are referring to) keeps every intermediate version of the state which is not necessary.
--no-ancient-blocks is less secure than a light client and is not recommended. It will however, drop your storage requirements to a few tens of GB. That means you grab a snapshot (including a recent state) and never check blocks before it to verify that the snapshot was valid. Warp sync doesn't calculate state for historical blocks, only verifying difficulty.