Would Matt Harvey pitch again if Mets were out of contention?

No.  It's pretty obvious that the only reason the Mets are not protecting Matt Harvey from himself is that the Mets have a short sighted objective of qualifying for the 2015 tournament and making the extra money associated with that, including more season tickets sold during the winter for 2016.

Harvey has now thrown 172.66 of his doctor defined limit of 180 innings.  Who in his/her right mind really thinks that Mets ownership, management and fans would be pushing for Harvey to pitch any more in 2015 were it not for the tournament?  James Andrews, you know, the one who actually went to the doctor school, has set 180 innings, give or take, as a cautionary practical limit, pitch count not withstanding.  Who wants to insure Harvey against injury if he pitches more in 2015?  Surely not the loudmouth media types who insist that there is no supporting evidence for the caution of Dr. Andrews.  And besides, they and the Met fans, do not like Harvey's agent Scott Boras ... boorishly referred to as Bor-ass in some fan circles.  Hey, there's a real reason to risk Harvey's career.  Met fans don't like his agent

Harvey pitched really well in August: one run (homer by Pirate Pedro Alvarez) in four starts; innings: 7,8,6,6; pitches: 88,97,103,103.

But in his two September starts:

September				Tm		Opp	Rslt	Inngs	Dec	DR	IP	H	R	ER	BB	SO	HR	HBP	ERA	BF	Pit	Str	StL	StS	GB	FB	LD	PU	Unk	GSc	IR	IS	SB	CS	PO	AB	2B	3B	IBB	GDP	SF	ROE	aLI	WPA	RE24	DFS(DK)	DFS(FD)	Entered	Exited
25	61	133	Sep 2	NYM		PHI	W,9-4	GS-7	W(12-7)	4	6.1	9	4	4	1	9	1	0	2.60	29	101	68	15	16	6	13	7	2	0	47			0	0	0	28	1	0	0	0	0	0	.58	0.057	-1.35	17.45	12.33	1t start tie	7t 1-- 1 out a3
26	62	138	Sep 8	NYM	@	WSN	W,8-7	GS-6		5	5.1	8	7	7	2	6	0	0	2.88	26	74	53	11	9	14	4	2	1	0	28			0	0	0	22	0	0	0	0	0	0	.79	-0.263	-4.43	0.40	4.33	1b start tie	6b --- 1 out d6

Eleven runs in 11.66 innings.  Pitches: 101,74.  Maybe Harvey will rebound and lead the Mets to a championship but it seems reckless to risk his career simply because the team inexplicably succeeded in 2015.  Neither Met management nor Met fans expected that.  But is it any reason to treat one of their players differently?  I think not.

And lest we forget:

Johan Santana April 5, 2012 by slgckgc via Wikimedia Commons

How Big A Deal Is A No-Hitter? Saturday, March 16, 2013

June 1, 2012 Johan Santana became the first Met pitcher to throw a no-hitter: 8-0 against St. Louis in New York.  Met manager Terry Collins let Santana throw 134 pitches even though Santana missed the entire 2011 season with a bad arm.  It is inconceivable that Collins would have let Santana throw 134 pitches in any other regular season circumstance... His final appearance was August 17.  Santana's ERA had risen from 2.38 after his no-hitter to 4.85.
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Santana never pitched again in the major leagues after 2012.  His career was over at 33.  With Minnesota Santana had won the Cy Young award in 2004 and 2006.