Would Wrestlemania, and ultimately the WWE not exist without the Andre/Hogan match at Wrestlemania III? Absolutely not. The WWE didn't really need Andre/Hogan at Wrestlemania III, to save Wrestlemania and the company. By 1987, the WWF was already one of the biggest phenomenons in American pop culture. They were already drawing big ratings on NBC with Saturday Night's Main Event. I believe Hulk Hogan's cartoon show was still airing, and Hulk Hogan was still a major pop culture icon, as were other wrestlers. The first Wrestlemania was the real "make or break" event for the company's history as well as Wrestlemania itself. If the first Wrestlemania had flopped that could've been the end of the WWE and the majority of us would probably not be wrestling fans. Even if Andre/Hulk never happened, WWE would still be going strong like it is today.
Would WWE still drew as big a house and made as much money on Wrestlemania III without Andre/Hogan being the main event? That I'm not so sure about. I believe that Hulk Hogan and the WWE were huge enough at that point that they could've put Hogan up against anybody and drew a big house, as Hogan and Paul Orndorff already drew a big house the previous summer in Canada. I do think that if they had had a final grudge match for the title between the two at Wrestlemania, that could've drawn as big as Hulk and Andre, because his feud with Mr. Wonderful did huge business. Along with Macho Man, Piper and Andre, his feud with Orndorff was his biggest feud of the 1980's.
But other than Paul Orndorff and Andre the Giant, I don't think anyone else up against Hogan would've drawn the 78,000 or 93,000 (whichever number you go with) house that the Hogan/Andre match did. Sure Jake Roberts was really over, but I don't think him and Hogan would've drawn as much as Hogan and Andre. While more serious, hardcore wrestling fans would've loved to have seen Bruiser Brody, Stan Hansen, or Harley Race go up against Hulk Hogan, your casual mainstream wrestling fans who got into it because of MTV, Mr. T, and Cyndi Lauper, etc. wouldn't have really cared near as much. In fact they probably wouldn't have even taken Harley Race seriously with the king gimmick. However if Vince had just let Bruiser and/or Stan Hansen be themselves, then they could've been considered serious threats to Hogan, especially Bruiser Brody, as he was a scary looking dude lol.
Macho Man Randy Savage was really over as well, however, I don't think a match between Hogan and Savage could've drawn 80-90,000 fans at that point in time, as their previous rivalry during 1986 was really more about just titles and one-upping the other. It wasn't near as personal as it would later get. Now if WWE had decided to have Wrestlemania V in a stadium in 1989, you bet Hogan and Savage could've drawn 80-90,000 fans. It might have even topped Andre/Hogan, I think.
While it's intriguing to think of possibilities for other opponents, I really don't think anyone, except maybe Paul Orndorff could've drawn 80-90,000 fans in the Pontiac Stadium with Hulk Hogan other than Andre the Giant. Andre the Giant was a pop culture phenomenon during the 1970's and early 1980's, when wrestling was very much a "cult" form of entertainment. So the older fans still loved and knew Andre. Andre helped draw that crowd, make no mistake about it.