They would,
it would be quite an interesting thing to see what would happen if a bunch of players from the Islands were able to go professional.
There have been several from French Polynesia who have played professionally in France over the years - most famously Christian Karembeu from New Caledonia who arguably had the most illustrious career of any player in Oceania history ahead of Wynton Rufer or any Aussies such as Kewell. A World Cup winner with France, European Champonship winner and two time Champions League winner (Real Madrid) and Oceania Player of the Year 1995, 1998. (Karembeu was eligible to play for New Caledonia since he grew up there before moving to France as a teenager).
Other island footballers who played professionally :
Pascal Vahirua (Tahiti): Played for twenty years in France, mostly for AJ Auxerre in French top flight in the 80's and 90's. Vahirua appeared for the French national team at Euro 1992 and qualifying for World Cup 1994 (22 games for France). Spotted by the Auxerre manager whilst holidaying in Tahiti.
Marama Vahirua: younger cousin of Pascal who has played professionally in French top flight since age 16: Nantes, Nice, Lorient, currently Monaco. Former France u-21 international.
Gerald Forschelet (Tahiti): Former Cannes, Bolton Wanderers, Neuchatel Xamax and Charleroi midfielder, still playing in lower Belgian leagues.
Nicolas Vallar (Tahiti) a defender at SCO Angers , at Montpellier Hérault Sport Club and FC Sète . He now plays for FC Penafiel , in Portugal.
David Grossman (Tahiti) : defender at FC Lorient 1992- 1998 (French Ligue 1 champions 1995), SCO Angers 1998-2001, Olympique Vannes 2003-2004, Olympique Saumur 2004-2007
William Bambridge (Tahiti) : Stade Rennes (Ligue 1) 1930's
Claude Carrara (Tahiti): FC Toulon 1965-70, Tahiti national team
Patrick Appriou (Tahiti): Olympique Marseille 1986- 88; played in the semis of the Europoean Cup-Winners Cup against Ajax 20/04/88. Olympique Ales (France) 1988-1990.
Reynald Temarii: former OFC President and Tahiti international (recently in FIFA strife) played in France from 1988- 1990 for Nantes.
Felix Tagawa (Tahiti international): Brisbane Strikers, Adelaide United Aussie NSL 2003, 2004
All of the talented Solomon Islanders like Bartram Suri, Henry Fa'arodo and Benjiman Totori who have played in NZ, Australia and Tahiti have spent most of their adult lives as professionals - they have been fulltime footballers with no other jobs usually e.g. I interviewed Bartram Suri in Nelson once and he was living in Hotel Nelson and paid to play for Nelson.
The Masi cousins from Fiji: Esala and Manoa Masi played for some years as professionals in the old Aussie National Soccer League: Esala for Gippsland Falcons 1995-97, Woolongong Wolves 1997-2000, Newcastle United 2000-2004. Johor FC Malaysia 2005 and various state league clubs; Manoa Masi for Gippsland 1995-97.
THE GREATEST UNKNOWN LEGEND OF OCEANIA FOOTBALL: ANTOINE KOMBOUARE (NEW CALEDONIA):
New Caledonia- born pro in Europe 1982- 1998 who won everything in France 1990-1995 with Paris- Saint Germain (Ligue 1, Cup) Also played for Nantes, Sion (Switzerland) and Aberdeen (Scotland). At the PSG, he became famous for a winning header he scored in the dying seconds of a UEFA Cup quarter final against Real Madrid, in the 1992-93 season. The header qualified PSG for the next round. Kombouaré had already scored a decisive goal in similar circumstances against Anderlecht in the previous round. His habit of netting tie-deciding headers earned him the name of "Casque d'Or", which means "Golden Helmet" in French. In 1994-95, during a UEFA Champions League quarter final against Johan Cruyff's FC Barcelona dream team, he captained Paris Saint-Germain to a resounding and unexpected 2-1 win which qualified the French side for the semi-final, which they lost to AC Milan.
Kombouare has had the greatest managerial career of anyone from Oceania, managing French top flight sides Strasbourg, Valenciennes (French second div. champions) and Paris-Saint Germain 2009 until January this year when he was controversially fired with PSG on top of the league and widely regarded to be playing their best football for decades (PSG's chairman connived to replace him with former Chelsea manager Carlo Ancelotti). PSG appeared in two French cup finals during his tenor, winning once and qualified for the Europa League.
Isn't it amazing we haven't heard of this guy in New Zealand when he's an absolute football legend?
Frederic Piquionne : New Caledonia-born West Ham team-mate of Winston Reid, prev. with Stade Rennes, Monaco, Lyon, Portsmouth; one France cap.
Benjamin Longue (New Caledonia): SC Bastia, France (Ligue 1) 1998-2005, CA Bastia (fourth tier) 2005-2008
John Gope-Fenepej (New Caledonia): Played for Nantes in France, Bolton on loan and Creteil in France.
Marek Aucher (New Caledonia): Stade Laval (France Ligue 2 ) same team as Eugene Dadi (ex-Wellington Phoenix)
Vincent Xati Taua (New Caledonia): In Italy 1998 to date. Striker played for third and fourth tier sides Cavese, Benevento, Vibonese and Teramo. Currently at Isernia (fourth tier Italy). Cousin of Christian Karembeu.
Three members of the current New Caledonia team currently play in the lower divisions in France e.g. Joel Wakanumune plays for Chambery, an illustrious French lower league club. In the 2010–11 season, Chambéry became the first amateur club in Coupe de France (French national cup) history to defeat three Ligue 1 clubs (Monaco, Brest, Sochaux), before losing in the quarterfinals.
KOMBOUARE YOU TUBE CHANNEL: http://www.youtube.com/topic/cHit39oEleA/antoine-kombouar?feature=relchannel

Kombouare - PSG manager 2009- 2012

Kombouare - PSG player 1990- 1995
Big Pete 65, Christchurch