The two side boosters will need some kind of aerodynamic protection, which could very much be recovered with the rocket in one piece.
Will they be recovered and reused?
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The caps on the side boosters of the Falcon Heavy are attached to the cores and will not detach. Not sure that counts as a fairing in the traditional sense.
The term fairing, is traditionally used to refer to the protections around the second stage.
One of the Go Searcher recovery ships has been seen with a steel structure on the deck that is suggested to be a storage rack for either the recovered fairings, or a underpinning for the 'bouncy castle' designed to catch them.
The bouncy castle approach seems to have been more fully implemented on Mr Steven, a fast recovery ship SpaceX is trying to use to catch fairings.
They tried to catch the fairings from the Falcon Heavy demo flight, and missed. They will get it next time I am sure. Here is the fairing floating along, minding its own business before being hijacked by Mr Steven.
Then they dragged it aboard, kicking and screaming I am sure.
But the other half clearly fought back and did not make it so cleanly.