It does in fact all the "round" objects on a fixed gear drivetrain make a big difference. A more round and concentric cog and chain ring will have a huge effect on a quieter, faster and more efficient drivetrain. Having used different cogs over time I noticed a difference when I switched to high quality stuff like the Sugino S3 cog and then the top upgrade to the EAI Gold Medal. The Surly Cog is a decent low cost cog if you need it but the Gold Medal is very well machined super smooth so the chain is gliding on it and gives me zero high or low spots so I can get proper tension. The chainring is Sugino 75 but I will say for a lower cost or 130bcd option the Sugino Messenger is a great way to go.

A good lockring is important though and everything else said looked good.