Yes! It's highly recommended actually.
You’ll need to keep in mind that any computer where you would like to access your budget needs to have either Microsoft Excel 97 or greater or OpenOffice (depending on which version of YNAB you’re using) or YNAB Pro if you are using the stand alone version.
The advantage to having your budget on a jump drive is that you can have it with you at work, at home, on vacation (alright, really…maybe leave it at home if you’re going on vacation), virtually anywhere. Again, it's highly recommended. Make sure you periodically backup your budget file somewhere else besides the jump drive just in case you lose it, it becomes corrupt…anything Murphy-Like happens.