It depends. Some systems don't show a file as available until they are done being written. Others lock the file as it's being written. For still others, the file is available as soon as it's created. You'll have to determine which type of system you're dealing with and respond accordingly.
Since there is no problem with the first case, I'll only discuss the second and third cases. If GoAnywhere tries to download a file that is locked, it will throw an error that you can handle if you so desire.
In both the second and third cases, you may want the vendor to write a small control file once the file/files you are wanting is/are complete. You can then check for the control file, and if it's there, download the files you're looking for.