Depends on what year of TDI

After 06, TDI engine is very quiet. When it is in low rpm, say it is idling or waiting in red light, you can hear engine diesel unique sound, but once you start to run, the engine revs up to 1500rpm or beyond, TDI engine becomes just as quiet as gas engine, you can't tell the difference in noise level. At that time, the road noise is bigger than egnine noise, what OP said is conditionally correct.

I used to have a 02 Subaru Forester, which was much noisier than my 06 TDI. Becasue of that, I sold it after 20k miles.