I doubt it, unless the USB port is ON the monitor, then it MIGHT be possible to have the USB ports sleep at the same time as the monitor, but even then most companies dont do that. I would think that the ONLY way to have this work would be to make it so the computer itself goes into stand by before anything else. Like, most power schemes have the monitor turn off before the system goes into stand by, but if you disable monitor sleep, and just make the system go into stand by say after, half an hour, that may work.
The only thing i see wrong with even this is a lot of the time keyboards and mouses are used to wake the computer up, by wiggling it or hitting a key, and many models of mouses and keyboards are USB, causing the computer to keep those rails on while in stand by, which would also power your led strip, even in stand by. I'm thinking this may be a lost cause unless there is some specific software someone knows about to do this.