Not without building a custom script to do the counting. This is how monitoring downloads works.
When the URL of the file is output to the page, instead of the actual URL of the file like http://yoursite.com/path/to/file.pdf something like this is used for the url http://yoursite.com/download/script.php?file=123 where 123 is the ID of the file to be downloaded. Of course these are not the actual urls or they could look significantly different.
The special URL is for a script or function of some kind on the site that counts the download and then returns the actual file with all the correct headers.
It might be possible to “cheet” this, depending on the file download monitor plugin that you using by seeing how it outputs the URLs for files to be downloaded and counted and then using the same URL structure when outputting the links to the files in ACF fields.
