Is it possible to persuade Vegas Pro 16.0 to monitor a directory, and if a file appears in that directory, encode the file with a predefined profile and destination directory?
Yes it is! But you have to write the script that will do that. Basically, you'd start your script and your script would keep an eye on that folder. When the file appeared in that folder (have to be careful as you have to wait until the entire file is there!), you would then have the script load it, render it as desired, clear the timeline, and then delete that file from the watch folder.
I was working on something like that for a specific machine at a place I worked. I got it functional but it was never put into service so my code does not have long term testing behind it.
Just be aware that you can't use VEGAS for any other purpose while that script is running.