No, Tempotreadle does not need to be hooked up to your computer. The only time you will connect TempoTreadle to your PC or Mac is if you want to install a firmware update to obtain some future functionality that is released for TempoTreadle.
You do need to use your computer to load your designs onto the Micro-SD card that is used with TempoTreadle. Once your design is saved, take the Micro-SD card to the loom and insert the card into the slot at the bottom of the System Unit.
TempoTreadle does need power. It can run from USB power using a USB data cable (such as the one supplied) that runs to an AC adapter or a USB battery.