Yes. All the circuits I've seen use 12 at least. I've used 18 volts, 2 x 9 volt PP3 smoke alarm type, as the current drawn is quite low.
I needed noise for a deep dive on another topic. I remembered and obtained some copies of the old MM5437 Digital Noise Source, thinking that it would suit a 5-volt only project better.
Imagine my surprise and disappointment to find that that chip's clock varies with the supply voltage - to get the desired output you need to supply 15 volts. It produces a sequence that repeats at one minute intervals. Shift register too short!
a7