As mentioned, it isn't critically important to clean the gas tube to ensure function. Not much on the AK does. However, in the interest of being a competent and professional rifleman, maintaining gear is important, so the gas tube should be cleaned with the rest of the rifle. Finding a big enough patch might be difficult.
I spray mine out with a chemical degreaser like Gunk Out and place it on a rag propped up vertically so it can drip out. Every couple minutes I'll run a 12 gauge Bore Snake through it, and repeat this process until the drip isn't black anymore. Then I just run the soft "rope" section of a 12 gauge Bore Snake through it a couple more times to dry it out. Like the gas piston, chamber, bore, bolt face, and firing pin channel, the gas tube should be kept clean and dry.