Yes! Just ensure photographers follow the proper procedures when shooting the cards. And upload images to your Project as you normally would one camera at a time.
Snapizzi utilizes EXIF data in your image files to identify multiple cameras and index your Project properly. There really isn't any reason to rename files prior to uploading to Snapizzi, but if your workflow includes renaming prior to uploading, be sure that your filenames include leading zeros equal to the highest number in the sequence (e.g., 0001 - 9999 rather than 1 - 9999). Your Project will not index properly otherwise.
Lastly, ensure that the time on your camera is set properly so timestamps are accurate in the image file EXIF data.