No they wouldn’t, it would, at most, be a deadlock between the three parties that the House would decide on. One would hope they would go with the one with the most votes, but in reality they can pick anyone. Including someone who wasn’t even one of the top three candidates.

Not to mention all the people who want a “third party” aren’t necessarily going to vote for the same third party. They all want their own person. Most likely none of them would get anywhere near the majority popular vote, much less any electoral votes.