No, cards Set Aside cards are not In Play
The Seaside Rules states rather specifically on page 4 that set aside cards are not in play, only played cards are.
In play cards are those you have played - not those set aside, trashed, or discarded. Nor are they cards in your hand, deck, supply or discard piles. (page4, sidebar)
“In play” -- Action cards and Treasure cards played face-up in a player’s play area are in play until they are moved somewhere else—usually until they are discarded during a Clean-up phase. Only played cards are in play; set aside cards, trashed cards, cards in the supply, and cards in hands, decks, and discard piles are not in play. Reaction abilities like Moat's do not put those cards into play.
Island – [...] Island and the card set aside with it are set aside face up on the Island player mat provided. They should not be shuffled back into your deck when you shuffle your discard pile. [...]
Additionally, the Intrigue rules, define Set Aside (page 4, Intrigue), and instruct you to not follow rules text for cards set aside. And while play is never defined in the rules, it is only used in two contexts while appearing 63 times (3 if you count the single instance in the sidebar, "play passes clockwise").
to play (verb): to place an Action card from your hand to the play area, and follow the instructions on the card or place a Treasure card from your hand to the play area adding their value to any coins provided by action cards then Gain any Card from the supply of equal or lesser value.
play area: the place where Action cards and Treasure cards are placed during a players Action/Buy phases. These cards are usually placed in a player's Discard during the Clean-Up phase.
In the Action phase, the player may play one Action card. [...] To play an Action, the player takes an Action card from his hand and lays it face-up in his play area. He announces which card he is playing and follows the instructions written on that card from top to bottom. [...] Any Action cards played remain in the player’s play area until the Clean-up phase of the turn unless otherwise indicated on the card. Players should not discard the cards prior to the Clean-up phase, unless directed to by the card or another action.
In the Buy phase, the player can gain one card from the Supply by paying its cost. [...] The player may play some or all of the Treasure cards from his hand to his play area on the table and add to their value the coins provided by Action cards played this turn. The player may then gain any card in the Supply of equal or lesser value.
"Set Aside” – when a player sets aside a card, he places it face-up on the table (unless otherwise indicated) without following any instructions on the card. An Action that requires a player to set aside cards will instruct him on what to do with these cards.