I don't see a superlative boxing talent with him and I don't think in an alternative career path he'd ever be the best guy in his (very competitive) weight class. But he'd be a great pro prospect. Any guy with that kind of work ethic, balance, strength, competitive nature and cardio who walked into a gym and wanted to fight would get the attention of the trainers there. Anyone who says otherwise is advertising how much they know about the fight game. There are a lot of pro boxer, only a few dozen champions and only a handful of HOFers. Being a solid pro is impressive, even if it doesn't put you on par with Floyd Mayweather.
An athletic guy who can push a pace and take a punch is going to win at the early stages of competition. Edgar could almost certainly be the guy who beat out of town journeymen at the top of a card at the local VFW. How he would do after that is a question. If you transposed his MMA boxing technique to a boxing ring the answer is "not very well" but Matt Lindland showed even crappier wrestling technique in MMA before and after winning a silver medal in wrestling. MMA is MMA and every "feeder" style is going to have to be adjusted to be successful. I don't know how well Edgar's MMA boxing would adjust to straight boxing--that's the big question IMO. If he can adjust well, I could see him as a fringe contender in boxing, a top 30 guy who doesn't get tired and beats prospects who show up out of shape and/or expecting an easy fight but losing to focused guys at the top level. If he can't change the way he boxes then he loses to a lot of guys, including many who aren't full-time fighters.