Yes, but you will need to rig something up to hold the material at the correct height that it would have been if the crumb tray was in there, and you need to put some material down on the bottom so that the laser beam isn’t bouncing off the metal.
There is a writeup on how to cut without the crumb tray here, but it is an advanced technique that might be a little difficult to pull off if you haven’t done any laser cutting before. You might want to just wait for the support team to get back to you on when the tray is arriving, or wait until it shows up.