I have 2 of these with e-sata connections that I use for archive purposes and find that the drives do get quite hot when transferring files or on occasion using them for a quick access for a video project clip...I have taken to running a fan on them when they are used to keep the temperature down. I've not had any ESD issues with them since I started using them, but my environment is not a high static causing one (no carpet, lower temperature and good humidity). I looked at mine to see if I could find the screws you are talking about and couldn't...plus all the connections and power switch for the unit is on the same side as the open back of the drive when in position. This sounds like something you would need to fabricate if it bothers you...I am not imagining it would be too difficult to make something like that...perhaps just a cut down piece of perforated aluminum screwed or epoxied to the unit?
I have two of these docking stations, each a dual SATA dock. One is USB2 and the other is eSATA.
I use the removable drives for all my projects and backups. Every client gets a disk drive assigned to them, so when I work on a client project, it's a simple process, drop the client drive into the dock, turn on the power to the dock, work on project.
I have a couple of dozen drives in my drawer and never had a failure yet.
But, on your original question.....
If you did screw some kind of shield to protect the electronics on the drive - you would never get it into the dock.