I have no hard drive installed, Only USB thumb drive. Will this be a problem?
It will work just fine. I've often used it as a tool to diagnose computers with hard drives that have quit working.
If you want to save stuff, you could plug in a thumb drive or a USB hard drive and save it to that. A thumb drive will show up just like it would on a normal Ubuntu install.
Another option if you want persistence is to make a LiveUSB drive with Ubuntu's startup disk creator and use the option to have persistence.