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.