Is it possible to put an original Floyd Rose in an Ibanez RG370DX Edge III bridge without routing it?
if you can, take it into a guitar shop and compare the route size of a guitar with an OFR and yours to see what the size difference is.

and buy an Original Floyd Rose not a Kahler, just stick to the people that invented it. they run about $150
The only way that you will know it is by stripping apart your Edge III and measure the Ibanez routing. Compare it to Floyd Rose's routing template here - http://floydrose.com/instructions.html
The most trusted LFRs are Kahler and Schaller so it shouldnt be much different from the OFR.
"Play with your ears" - Yngwie Malmsteen, Paul Gilbert
Thats what she said...