Sure (and to some extent, Obama did it in '08, and Bernie did it this year). It's 100% reasonable to run a campaign on a message of "My opponent is funded by $BANK and $PHARMA and whatnot. I'm funding this out of my own pocket / I'm funded by small-dollar donors / My entire staff is living off of ramen".
Does it single-handedly win an election? Probably not. Does it win some # of votes? Most certainly.
Does it single-handedly win an election? Probably not. Does it win some # of votes? Most certainly.