Saving Media Cache to External Hard Drive

I have a very large project for my senior thesis film that I am editing in Premiere Pro CS6. I have all 200GB of video files organized on my external hard drive.

I use my laptop, my co-editor's laptop, and several of the school's Macs to edit. Each time I use one of these computers, the project has to conform the audio and generate a peak file, which is very time consuming. Often, it will also make me locate several of the video files form my project (sometimes all of them), which is also an issue.

I finally figured out the language of this to find in the forums that some people suggested changing the Media Cache files and the Media Cache Database to the external hard drive. When I contacted Adobe Live Chat, the representative cautioned me not to do that because:

So allegedly, that will break the workflow of Premiere Pro...

Instead, they had me go into Project>Project Manager and change the settings for "Resulting Project" from "Create New Trimmed Project" to "Collect Files and Copy to New Location."

This results in all of the video files that I have imported into the project being copied to the same folder that the project file is in. This seems counterintuitive because all of my video files and media are located on the same external hard drive already.

This is what I would like to redirect to my external hard drive:

My question is this: Are there any risks with saving the Media Cache files and the Media Cache Database to the external hard drive? Was the representative correct in that it can cause the project and Premiere to crash and not open?