I think it depends on a few things.
1) The fandom in question.
2) The timing of the sudden burst of popularity
3) The quality of the writing
To explain:
First, a super-active fandom is the fandom most likely to take a pairing and run with it. If you try to write stuff like this for a much more quiet fandom, they're not exactly going to pick it up and run with it like a fandom that's always doing something would.
Second, kind of related to the above, it has to happen at a time when the fandom is paying attention to its fanworks. If it's during a slow period, it probably own't take like it would when the fandom is buzzing with activity.
Third, no one's going to read shitty fics, so ideas presented within will likely be ignored or missed entirely.
As a member of the My Little Pony fandom, we saw this go down several times when the fandom was at its peak a few years back. Characters like Lyra and Bon Bon were just typical background characters with tiny quirks that showed up from time to time, but the fanfic writers decided to ship them, and suddenly it got immensely popular, and now LyraBon is practically canon within the show (the same thing happened between Vinyl Scratch and Octavia, where they became a super-huge pairing partly because of fics like Allegrezza and The Vinyl Scratch Tapes, culminating in them living in the same house in the show, but there's still a lot of people who don't see them as romantically inclined, but simply platonic roommates). Hell, it even extended to Cargo Ship or Crack Ship pairings, like Princess Luna and an abacus and Rainbow Dash and a kitchen sink, and even Fluttershy and Anon ("Are [silly things she's trying to do] you fetish?")
So yeah, it's possible, and it's happened, but it would need a few things to really catch on.
Qui odoratus est qui fecit.It doesn't seem too common for fanfics to get everyone hooked on a ship that no one cared about before, but they can definitely make ships more popular if they already had fans. As mentioned before, though, it depends on the fandom.
It's also worth mentioning that if you have a small or midsized fandom with a handful of authors who are way more prolific than everyone else, it'll skew the numbers towards whatever they like, regardless of how much overall support there is for the stuff they write about. That can be true for shipping, or it can be true for other things.
Fandom-specific plots tend to be either Follow the Leader or everyone jumping on the same source of Fanfic Fuel at once. Sometimes both. So yes, sometimes it's a concept that someone did really well and other people liked enough to try their hand at, or incorporate parts of into their own fics.
edited 4th Jun '18 10:18:56 PM by SapphireBlue
This is something I've wondered about for a while, if fan fiction can influence others in the fandom. Like let's say there's a small group of fans that really likes one pairing. Now let's say they write a lot of fan fiction. Is there a point where others will get behind that pairing? Does there even need to be that many fanfics? I guess this doesn't necessary apply to only pairings. It could also happen with crossovers or a Fandom Specifc Plot. Thoughts?