It’s theoretically possible. I know that you can set up severs to have a default ‘This domain doesn’t exist, even though DNS says it lives here’ page, but honestly they’re really hit or miss.
The heart of the problem is we’re not really in charge of DNS propogation. No one-person is. When we move you, we lower the TTL on your domain, so that tells everyone “Hey, keep this information is only valid for X hours” (on a major move, I’ve seen it dropped to 5 minutes). Then, as each DNS server connects to your domain, it checks “Has it been 5 minutes? Let me see what the IP address is and update!” It then caches the information until the next time.
Now, no matter how low we set that, it can still take 72 terrible hours to push out world wide. It usually doesn’t, but that is the maximum time allotted. In part this is because of the caching. Caching is good, though, since it makes everyone’s sturdy tubes that much faster, but in these cases, is totally frustrating.