At least in the US at the federal level, certainly not.
They just aren't the people that will change campaign finance reform, build walls, or raise the minimum wage. That is kind of what congress does. So you could elect any president and only see legislation they want passed because either they bargained with the other party in congress or their party had a majority in it already to pass the legislation.
It is only force of habit that most people expect the president's party to go with their policy ideas in congress. If Bernie were president, for example, you would not expect the Dems or Reps in congress to ever support him on anything, because hes anti-establishment.
Toward the end the study notes: "When the preferences of economic elites and the stands of organized interest groups are controlled for, the preferences of the average American appear to have only a minuscule, near-zero, statistically non-significant impact upon public policy."
At the national level, US democracy is an illusion.