Not true. See https://youtu.be/DU-HruI7Q30 as posted by someone else. If the machine was really busy doing other stuff, you'd have trouble, but if the machine is MOSTLY idle, apart from running GPG on your chosen cyphertexts, then occasional network interrupts and short-lived cronjobs and stuff won't be too much of a distraction. He even demonstrates that his machine is running something really short every second, doesn't matter, you can trick GPG into making your machine emit the tell-tale squeals for a decent fraction of a second, telling you about ONE bit of key. Repeat with carefully selected cyphertexts and you can extract 1 bit per second until you're done with a 4096-bit key in about a hour. The example in the video had GPG in Enigmail in Thunderbird decrypting your email on receipt. If you know enough about SSL you could fairly easily do this as a series of negotiations on any TLS port.