You could do that in theory, but only in theory because there are some reality checks in there.
1) you will need a cellular plan that has truly unlimited, unthrottled data
2) there are many parts of the country that still do not support enough 3G/4G/soon 5G speed to upstream continuously. You would be reconnecting manually in your youtube account all day long as you move about.
3) If you are going to stream form a mobile device, YouTube requires that you have at least 1000 subscribers. This does not apply to desktop and laptop devices.