No, this won't work. You can't just hook up raw USB signals up to a TTL-level chip and expect it to do anything meaningful. Even if the signals were powerful and noise-free enough for it to do anything, USB's got a very complicated protocol to the point it expects you to tell it how much power your device will consume before it's willing to give you the time of day. You'd better just get an adapter of some sort if you want to make USB controlled leds a project and not a career.
I've used the
DLP-IO8 module before and reccomend it. It's pretty simple to use and flexible, plus works with Linux and Windows(uses the FTDI USB-to-serial chip). It acts like a serial port when plugged in. Set it to 115200 baud no parity 8 bits 1 stop bit. Write an ascii '1' to the device and it sets pin one high, write an ascii 'Q' to it and it sets pin 1 low, etc, etc. Other functions include analog input and digital temperature-sensor reading. It provides convenient power hookups. And it's shockingly cheap for what it does. It should control your LEDs fine.
