Q: Is a No Battle/Encounter Hack possible?

I have to agree with Tenkarider, the whole idea would be very, very, boring.

I don't agree with you in full here. While this would be boring for me or for you, I know people that pretty much just play these games for the exploration and the dialogue. This hack would be pretty much perfect for them. From their perspective, the main problems that I see with it would be that; a) You can explore, but in dungeons it is pretty worthless as you won't be using anything you find, as nothing helps you progress or explore anything else further; and b) Without as much in between cutscenes you wouldn't feel as though the game is very large from the perspective of metonymy. So even if we're not going to play it, that doesn't mean that it's not worth having, if the OP is going to do the legwork.

And this is definitely possible to do, provided you're willing to do a lot of it yourself. Cheat codes/FF3usME to get the Moogle Charm and OP characters would definitely work for a quick fix for the OP's personal use, but the laundry list of instructions on what to do with them (like turning off the cheat code for random encounters at the part where you're supposed to get Gau) would probably intimidate non-gamers as well, I suspect. It wouldn't seem like much for us, but I can see somebody already reluctant to play one of those "newfangled video game things" getting scared off by a one to two page ReadMe of instructions.

To eliminate some battles, you could just remove them with the LE (like for Atma Weapon and Inferno), and for others you could always edit their HP down to one in FF3usME, in general (although Vargas should have more than that), and probably lower their level to one so that they can't do any damage before dying either. Perhaps consider allowing either form of Chadarnook to die as well. For Gogo just use FF3LE to create an entrance to his cave on the overworld (there's a pretty good spot on the mountain to do that). Gau should probably be in the corresponding world's Cave on the Veldt, where he should probably initiate a short event that simply initiates battle with a formation consisting of only himself. That would be the hardest thing, probably, as it would require some event editing (there's a tutorial on the site). Hopefully that covers all of the bases here. I suspect all of that should be within the reach of somebody who hasn't done any hacking before, with the event editing being the possible exception, but that's a relatively easy event to create, and if you get that far, you'll definitely get more help at that point. Removing things from the game is always easier than adding them.