If by "pollution" you mean carbon dioxide release:
The Eco Guide discusses the amount of CO2 generated by coffee from growth through shipping to processing and the machines in the cafe where you drink it.
In Examining the Carbon Footprint of Coffee it says
This comes out to approximately .275, or about a quarter a pound of CO2 is produced for every cup we drink.
This is 125 gm per cup.
The UK Goverment website gives the average CO2 emissions for new cars in 2015.
In New car carbon dioxide emissions it says
The average carbon dioxide emissions of cars registered for the first time in the second quarter of 2015 (April to June) was 122.1 grams of carbon dioxide per kilometre.
This is 1221 gm per 10 km.
The amount from the 10 km drive is ten times greater than from the coffee, yet
the assessment for coffee included every accountable source of CO2 from bean to cup
the assessment for a car journey is only the actual fuel burnt, not its extraction, refinement and distribution, and not the manufacturing emissions of the car itself
Even without those overheads, the car is far more polluting.
So based on that, the answer is no.