Not quite. Lets imagine a scenario: Its election day 2016. Four candidates are running and nobody got a majority of the electorate. The House of Representatives will decide the next president HOWEVER its the Representatives that were elected in 2014 (House of Representatives have 2 year terms). The 2016 version of the House doesn't take office until February of 2017. So image Clinton gets 49% of the electoral votes and the Democrats take the majority in the House. The current House majority are Republicans, and its this House that would decide the President, and there is a 0% chance they would vote Clinton. Even though a few months later the new Democratic House members are sworn and and would have voted for her.
The way the Constitution is set up is each state gets a number of electoral votes and you need a majority of these to become present, which right now is 270. The electoral votes are divided between the states based off population, so states like California and NY have a lot more than North Dakota. But, the constitution doesn't tell the states how they are supposed to use their electoral votes (most just do it by popular vote within their state). There is a sorta loophole to force the US into a straight up national popular vote system called the National Popular Vote Interstate Compact. The states in the compact would vote for the candidate who won the majority vote nation wide. If this compact reaches 270 electoral votes in strength in comes into effect and we got ourselves a popular voting system. Right now 165 electoral votes are in this compact, and 104 votes worth of states have it in pending in their legislatures. (and again this doesn't take effect until the compact has a strength of 270 electoral votes)
And of course, even if those 104 join the pact, that only adds up to 269. We'd be one vote shy.
And people don't understand our system because we use words differently than other countries. Much like "state" in a lot of the world refers to an independent nation, it doesn't here.
See, here we have "parties," but they're not parties like the UK, for instance. They're closer to coalitions, where multiple parties team up for common ground. This is clearly good game theory since team-ups will stomp out lone parties. In the US, we've got environmentalists, social justice folks, liberal economic theorists, labor, etc.. in the Democratic Party, and we've got the religious, conservative economic theorists, capitalists, etc... in the Republican Party.
The Dems are a tight coalition. Not a lot of squabbling (I can guarantee no one will even remember half of Sanders' attacks in a year, let alone 4). But the GOP? This is a coalition split right here. The Trump wing just can't work with the business wing anymore. The divide over social vs. economic interests has fractured that coalition.
So, parties aren't exactly some scheme to control the world or anything. If we got rid of FPTP, we'd just end up breaking up the RNC/DNC into smaller parties, which would then (if they're smart) form right back up into a "coalition" instead. And since that's functionally the same thing as the parties right now, and I'm not a prescriptivist, I don't see much to do.
On topic: Romney doing this is too late, but it even if they ran him under some other party's banner (like the Constitution Party), he'd flop. Might win a few states, but he'd only be stealing from Trump. Hillary would end up taking any of the toss-up states (which aren't the usual OH/FL/CO but instead former hard-red states like GA/MS/UT). She'd hit over 400 EVs if they split the vote.
And since Trump would know that he was going to lose in that situation, he'd torch the party so badly they'd need decades more to recover. Remember: Trump isn't a politician, so he doesn't care about burning bridges. It's not like he's ever got to work with these people again. If they screw him, he can tell his supporters to unregister as Republicans en masse, then laugh at the damage. Then he fucks off to one of his hotels while Priebus tries to repair their image.
For the RNC to weather this storm, they have got to make sure Trump legit tries to win. No letting him spend in NY or CA (he'll want to), no losing red states (Hillary will fight him on this), and try to keep the gaffes to a minimum. If Trump feels screwed, then there's nothing stopping him from doing as much damage as possible.