I don't think he would have, if anything he embodied what Turner and Bischoff were trying to get away from... the "Southern" associations that WCW had.
Sure Lawler was a draw in those areas but for a company trying to break a stereotype he was the polar opposite of what they needed. They went for guys like Davey Boy Smith, Hulk Hogan, Randy Savage and got Flair back after WWF runs to make WCW "appear national".
Lawler could have worked fine in WCW as an upper mid/semi-main event heel just as he did in the WWF... but he would have been fed to Hogan and the like, and probably Duggan and the other ex-WWF guys rather than seriously pushed.
Ironically, despite already being national, the same "southern-ness" was actually something the WWF was embracing at the time, they were bringing in more regional talents like Jeff Jarrett, Lawler, Cornette, Matt Borne as a way to balance out the cartoonishness with solid wrestling talent. While not being hired for specifically being southern, guys like Lawler and Jarrett appealed to those areas that WWF was expanding into more often than previously and someone like Borne, despite being in a totally gimmicked character as Doink, had the wrestling chops to counter... however silly those initial runs were for Lawler, Jarrett etc at times it was always clear they could wrestle and hold their own in the WWF.
From Vince's side both USWA and SMW were offering solid mid card talents with potential at good prices and value for Vince. For Lawler it was a win/win. He got national exposure on a part time basis allowing his own Memphis business to continue with the assists from WWF talent stopping in. Look how many talents came from that USWA/SMW period starting in late 1990 through to 1994... Kane, Papa Shango/The Godfather, Al Snow, Men On A Mission, Tom Prichard... with the exception of Mo... all of those guys had LONG WWF/E careers or multiple runs... their initial gimmicks maybe didn't wash but grew into important parts of the roster...just like Lawler did. If anything it's very shrewd business from Vince and the best return on talent investment since he bought Stampede. While those guys didn't really all "main event", they all became long term assets... some like Snow and Prichard were the cornerstone of their training for years... Vis and Charles Wright on the roster for years in strong roles and Kane speaks for himself... they all came from that initial punt on Jerry Lawler, seeing it could work, then translating it to Cornette and later Heyman and ECW. Lawler deserves a LOT of credit for shaping how the modern WWE operates as USWA was the template "developmental" territory and he was smart enough to take his own ego out of the equation when it came to pushing talent. Sometimes Cornette and Paul E didn't. WCW wouldn't have done that, they'd have focused on monsters to face Hogan. Imagine if some of those guys had gone to WCW how different things would have been...
Lawler may have ended up on the mic in WCW too, but it wouldn't have been the same as working with Jim Ross. Indeed as the Monday Night Wars show is constantly saying, "WCW didn't want a Southern accent", while Vince wanted out of the booth and Lawler and Jim Ross were a natural and fan friendly pairing after trying guys like Perfect, Savage and DiBiase. They became that Monsoon/Heenan pairing that had been missing.
Jerry Lawler is one of the better success stories of the "territory" talents in the big time. He had better feuds and matches, particularly with Bret in 1993 than Dusty and Harley race managed in their whole tenures and he had the "mic skills" in his locker to enable longevity. Dusty and Harley struggled in that first run and with the "hazing" and ran back to WCW, ironically becoming little more than off-screen agents. Lawler had it too, people shitting in his crown etc... but he saw the bigger picture, did as he was told and was very much "in on the ground floor" of the post Hogan era... when guys started jumping to WCW, he had a few years "loyalty" built up, and thus he was set and even if offered a jump could say to Vince he'd stay and be rewarded.
Lawler in WCW lasts 2-3 years tops till Hogan, Flair, Duthy and all the other politicking gets him fired or let go...all would have been jealous of his Memphis business and the whole "You never beat me" thing he had with most of them...they'd have been out to get him.
With the exception of that period he left for his wife (which again probably got him his job back in the end, Vince would respect standing up for your family) he has been in the WWF for nigh on 20 years... He'd never have got that in WCW... for all his pre WWF successes, Andy Kaufman etc... Lawler is defined as a WWF lifer in many ways, for a guy who was in his forties when he debuted, that's good going!