Yes, this is possible.
This information is available to you in the form of a FILELIST variable. The Number of Files transferred also becomes available to you as well.
On the OUTPUT VARIABLES tab when doing a GET/PUT, there are 3 variables available to create. Source FileList, Destination FileList and Number of files transferred.
Once the files have been retrieved, you can do a FOREACH loop across the Destination FileList Variable created from the FTP|Get. This gives you access to all the file attributes (ie., Name, size, last modified date, extension, etc.) and write that to a CSV, flatfile or even a Database table.
Please review these Tips & Tricks articles from our Forum for further information:Using FileList via SFTPTaking Advantage of FileList Variables