After comparing the happiness score and Human Freedom Index it could be said that probably yes. The correlation is 63%, so we might say that people in freer countries consider themselves happier.
What: Happiness score from World Happiness Report and Human Freedom Index
When: 2016 for Freedom and 2017 for Happiness.
Where: 147 countries of the world
Source: WHR and The Human Freedom Index 2018: A Global Measurement of Personal, Civil, and Economic Freedom