A finite-length sample of the most perfect white noise will not attain maximum entropy. You mention a lowpass filter -- that's accomplished through the sampling frequency. But your proposal is an effective lowpass filter, as any frequency longer than the sample length will clipped to exactly the sample length -- which you'll be able to hear as a distinct rhythm if it's a sub-audible frequency, or a tone if it's shorter.
Well, Spotify serves lossy compressed audio anyway. I don't know much about audio compression, but presumably it's first bandpass-filtered, and then filtered to remove psycho-acoutically unwanted audio components, and then compressed as a bitstream.
Taken to the extreme, you're looping a single datum: https://imgs.xkcd.com/comics/random_number.png