HFT requires low latency on their
reactions, not the entire transaction. In IEX's situation, there are two major cases --
(1) A person decides to cross the spread on IEX first -- in this case, their order will be delayed by 350us (or whatever the shoebox delays), and no one in the world sees the result of their trade until the public data feed updates, in which case all participants are reacting off the same feed, same as any other US equity exchange.
(2) A person hits another exchange first, in which case HFT races to cancel their orders on IEX or cross the spread against another firm's orders on IEX -- yes, their action is delayed by 350us, but so is every other person, so you're otherwise racing to get into the message queue at IEX, and the artificial shoebox delay is irrelevant, since all market participants are equally delayed by it.
So while IEX's shoebox delays the latency on the result of an action, it doesn't make an appreciable difference in the typical HFT strategy. The primary difference is in (1), there is a higher chance that an unsophisticated large block trader (because a sophisticated one will have already set up the necessary delays to hit all exchanges simultaneously) will be able to hit market makers on both IEX and other exchanges before anyone has the time to react, thus being able to take large advantage of their own proprietary knowledge (their own order) some percentage of times more often. The only thing this results in a decrease in liquidity on IEX, but seeing as they're a dark pool/minor player anyways, the difference is negligible.