This article may help if you are thinking of using twin or balanced line:http://home.comcast.net/~hamlakemn/AH-4_General_Information.html
The EDX-2 is very similar to the AH-4, has 160 coverage, higher power rating, slight difference in the molex connector and pin wiring between the two, but otherwise they are interchangeable. It is rumored that Alinco subcontract manufacture of the EDX-2 to guess who, but I can't confirm that.
The problem you may have is that this kind of tuner is designed for single ended or unbalanced antennas. If you use balanced feeder then you must 'float' the tuner from ground. You may have RF feedback via the coax or control cable, but this can sometimes be controlled by inserting baluns or ferrite clamps.
Another possibility is to insert a balun of this kind between the balanced feeder and the tuner:http://www.balundesigns.com/servlet/the-98/isolation-choke-balun-common/Detail
Going back to your original post, if you are using coax, then you should not ground the tuner, otherwise your G5RV will in effect be a loop with one side grounded! The instruction leaflet emphasises the fact the tuner must be grounded, this is for both transmission and safety reasons.
All in all, while you may find the tuner works in your particular application, it is not ideal for this use and not what the tuner is designed for doing.