Can I create an upload form that allows users to upload files of any type, and then process them based on their filetype?

Yes, this is possible because all Transloadit robots ignore any files they cannot handle. Therefore, you can set up two Steps with different robots that have use: ":original" specified, and the files will be automatically routed appropriately based on filetype. For example, if the uploaded file is an image, it can be resized and stored. If it is a video, it can be video encoded and have thumbnails extracted and stored. If it is a Word document or spreadsheet it can just be stored, etc.

See also:

Can you delete temporary files sooner? Is the data volume reset monthly? What's the difference between Uppy and Transloadit?