Not really. Capacitors form up in a fraction of a second - there's actually a formula for it. If they even turned it on at the factory, the caps will already be formed up when you get it.
Part of the durability of this myth is that components slightly change value when they change temperature. Of course, things might sound slightly different when something is hot. Not necessarily better, but different.
After a certain amount of exposure to heat, components permanently change their values. You can look at this as "burn in," or you can look at that as a component that is now defective because it is out of manufacturer's spec. Most gear will continue to operate with components out of spec, but they won't be performing at the level they were designed to perform at. My take is that when components change value, they should be replaced.
By the way, if anything thinks that it is a good thing when components are damaged and change to a different value, boy, have I got a deal for you. I've got a bunch of resistors and capacitors that have been "burned in" for 50, 60, sometimes even 70 years. They are so nicely burned in that they're nothing like what they were.
Even though they produced a wonderfully "burned in" sound on my old tube gear, I nevertheless replaced them because - for whatever reason - I find that the old radios and stuff sound better with parts that are in spec. Of course, that's just an opinion and what do I know? My test gear tells me the stuff is working properly, but that's just a matter of personal taste, isn't it? After all, when your car starts running rough because the spark plugs are worn out and your wires aren't conducting very well, you just tell the mechanic that the car is fully "burned in" and that it works better that way. Because that's only the mechanic's opinion and it doesn't really mean that your car isn't working correctly. Besides, you once read an article about cars and burn-in, so you know what's going on.
I promise that these resistors and capacitors won't sound anything like their modern equivalents. However, these are sold as-is. if something stops working there's no warranty. Also, it might be a good idea to update the limits on your fire insurance policy.
kingtz, no, tubes do not require burn in. It can be a good idea to run them for 24 hours to check for infant mortality. If the tube is weak or has issues, it'll usually kick off in the first 24 hours of use. So if you have a limited time to return what can be expensive tubes, it's smart to leave them on for 24 hours. If they make it, you can usually expect them to have a normal life.
No, this is not done to make them sound "better." It's to make sure you didn't get a bum tube.
Like everything else, the longer and hotter you run a tube, the shorter its life will be. Almost all of the amps discussed here are auto-biasing, but many power amps are not. This means that you have to reset the bias point every so often because the tube is degrading over time. It's not a big deal, but if you're running a power amp, it is a constant reminder that your tubes are running down - not some magical means of making them sound better. Similarly, you can put a tube into a tube tester and measure how much life it should have left.