Ben Simmons is a phenomenally idiosyncratic talent, but the answer is, no.
We can look at stats all we want but from an eye-test point of view, the 6'10 point guard/forward wouldn't survive with the purple and gold.
Anthony Davis' paint presence and playmaking demands a capable shooter from fifteen feet to the three-point line, which Simmons wouldn't fulfill. This doesn't get any better with LeBron either since he historically thrives with a scoring guard capable of making a reliable jumper.
The amount of drive and kicks to an open Ben Simmons would cause absolute turmoil on and off the court especially with the media. Los Angeles is a hot-bed for scrutiny and Simmons wouldn't have any immunity unfortunately.
The best case scenario I can think of is to play Simmons as a defensive hawk. The lineup would need to start Davis at the center position followed by James, Ariza, Ellington, and/or Monk. I think Monk gets the start, he seems to be the guy that gets his energy as a starter even if he isn't playing over 25 minutes each night. Ultimately this lineup would need LeBron to play off the ball since he at least has a believable shooting stroke; we all know LeBron is in a different stage of his career and at this point it is almost 100% unlikely he admits an off-ball roll to Ben Simmons.
As the purple and gold head deeper into the playoffs we would see Simmons picked on by intelligent Western Conference defenses. This is a mess waiting to happen, and what concerns me the most is Simmons' disinterest to score the ball even in attacking positions.
Where do you think Ben Simmons fits?