I'm going to take a stab at this.
I think the problem is that the iPad version has no route to connect to the file. In the instance pictured above, you have linked to a file URL that is accessible to the desktop version, but Go has no way to connect to drive s: on your server/desktop.
Go doesn't act as a sort of front end for your desktop database; it is running its own instance of the database. Consequently, it's not like Go tells Pro to access the file and feed it to the iPad. Go is trying to access the file itself and can't reach it. Go has no knowledge of your file/network system or how to access things on it.
There are a couple of options that do work, although differently. The first is that you make these PDFs accessible over the internet via http, so that you can access them through a web viewer. Go will display them with a calculated URL similar to the one that you show.
The second is that you load these PDFs into a container field in the database, so that they are actually contained within the Go database itself. So, there will be a table that consists entirely of the PDFs and some kind of relationship key for each. The related container field can then be added to your main layout. Clicking on that field will then offer an "open" button for the PDF. Note that you can't just store a reference - you need to store the file itself.
One other thing that occurred to me, but I haven't tested, is that you could create a second database that was only those PDFs and establish a relationship to the records in the main database. Then, put the related field on your layout. That database will have to be shared as well, and opened automatically (see the FMP7 protocol in the development guide), so that when the main Go database tries to find the related information, it can access it through the local instance of that second database of PDFs. As I say, I haven't tried this, and can't vouch for it's viability.
Hope some of this helps.
Thanks for the reply Allan. Actually, I was able to get my script working on FMG as I had originally hoped. I simply had to install apache on my desktop so my iPad could access the files on the local network. It works great and makes FMG much more useful.