Correct. The chief difference between English and German in this respect is the use of spaces (and what is considered a word). In German, you can basically drop the spaces from a noun phrase and call it a word, but it's basically a low-consequence surface syntax difference.

Side note: ancient Greek didn't use spaces, and many other languages (Thai and Written Chinese are the ones with which I'm most familiar) either don't use spaces or make spaces optional. The distinction between a phrase and a word gets a bit blurry at times, and I find the distinction is seldom useful, particularly when making comparisons across languages.