I'm reasonably certain it's fictional.
First, it appears on creepypasta sites:
http://creepypasta.wikia.com/wiki/Squidward%27s_Suicide
http://www.creepypasta.com/squidwards-suicide/
It should be noted that Creepypasta.com has a tag for stories that are based on true events- a tag that
Squidward's Suicide does not have.*
Both sites have comments that discuss the merits of the stories. The latter is largely positive, while the former is far more negative.
It has a TV Tropes article on the story, in it's fan fiction category:
http://tvtropes.org/pmwiki/pmwiki.php/FanFic/SquidwardsSuicide
There is a MST3K-style riff:
It points out some of the more unbelievable aspects (would unpaid
really get to see unaired episodes?**)
Finally, there is a Reddit user who claims to be the original author:
https://www.reddit.com/r/self/comments/185hc9/i_wrote_squidwards_suicide_and_am_kinda_happy/
https://www.reddit.com/r/self/comments/185hc9/i_wrote_squidwards_suicide_and_am_kinda_happy/
They even posted a screenshot to back up there claim:
http://i.imgur.com/G1JjCK9.png
http://i.imgur.com/G1JjCK9.png
Even if the Reddit user is lying about being the author, this does seem to be the earliest post of the story.
The final comment under the picture also points out that the Stephen Hillenberg, the original showrunner, retired from the show after the first movie, further showing the inaccuracies in the story.
In sum, this is a story with inaccurate facts, questionable claims and seems to be largely understood to be a work of fiction.
*For those interested:
http://www.creepypasta.com/tag/based-on-a-true-story/
**They are
far too eager to call "unnecessary details" for my tastes, however.