I don't think anyone would argue third party candidates can't be effective spoilers. I think that's at least partially why they enjoy as much support as they do. But they're not serious candidates for the office and anyone that votes for them is likely helping the party furthest from their values.
Would still have to form a coalition with someone or be a lame duck or his entire term. Ultimately boiling down to being just another member of that faction. There's very little say or control.