You could use a thumb drive for that, provided that your Mac will load through it. Yes. However, in order to avoid changing your MacBook’s boot loader, I would recommend installing the boot loader directly onto the boot drive itself. Which means - when you go for the installation - to select manual partitioning (at the screen where it asks you where to install Ubuntu). I can help you with that if you like.
Also, keep in mind, the installation thumb drive has to be a different one, not the same with the Live Image. So, you can flash a 8-16GB USB stick and use your bigger one for the installation. 
In the installed version, any changes and additions you do to the system/kernel/modules, they all stick!