This question came up today at an account and I can understand why, the system that we're going to replace is over 10 years old!!!
Years ago before the digital age of copiers, the answer was no way no how. Most of todays copiers (which are all digital), allows for the user enable auto tray switching from one tray to another. Thus when one paper tray has emptied the copier will feed from the next paper tray that has the same size of paper that is loaded. The benefit is that you don't have to run back to the system to fill the tray that emptied.
In most copiers this feature needs to be turned on by the end user. I sell the Ricoh products and in those devices you'll need to access the "user tools" key, once accessed the end user will be able to allow "tray switching". If you're not sure of the correct setting call your sales person or call the company that you bought or leased your copier from and they'll be able to guide you through the programming sequence.