We can measure candidates' locations on the left-right spectrum. It is a hell of a lot easier if they have served in at least a state legislature, but we can at least put legislators on a left-right spectrum. In Congress, we political scientists mostly use the NOMINATE scale, developed by Keith Poole and Howard Rosenthal, but there are also times when something like the ADA (Americans for Democratic Action) or ACU (American Conservative Union) scores are useful. Essentially, they just put people on the left-right spectrum based on voting patterns in the legislature because everything else is at least a smidge bullshit, although some candidate surveys do OK (Project Vote-Smart is reasonably good).
Do centrists have an electoral advantage? Yes. Yes, they do. This has been tested, and replicated. Ansolabehere, Snyder & Steward, American Journal of Political Science 2001, Canes-Wrone, Brady & Cogan, American Political Science Review 2002, and lots of stuff since then. Centrists do better in elections. This was a prediction from Anthony Downs's An Economic Theory of Democracy way back in 1957, and it's true.
It's just that the effect is kind of small. That's not really what matters all that much in congressional elections. You know what does? In general elections, experience. Candidates who have never held office before tend to get their asses handed to them in the general election, unless they are facing equally unqualified opponents.
The Democratic Party has been tying itself in knots over whether or not to go through the purification rituals that the Republican Party has been enduring for years.
Here's what political science research says: centrism does help, electorally. Only a little, though. Experience matters a hell of a lot more.