Maybe, an engine could produce such sound, but why was it chosen (out of universe)? By no means, it looks futuristic.
Originally, George Lucas had seen a British documentary on PBS about the Battle of Stalingrad in World War II and had noted that the firing sound of some strange Nazi rockets was quite weird and interesting. Lucas mentioned that it might make a great sound for the laser gun and Burtt managed to find a copy of the documentary. He then set about finding sources that could emulate that sound. Luckily, at Twentieth Century Fox Studios, Don Hall let Burtt go through the Fox sound library, where he found recordings of some elephants that had been done for an Errol Flynn movie The Roots of Heaven . In that film, elephants stampeded and bellowed. with an almost shrieking sound (the same sounds were used for the dinosaurs in Journey to the Center of the Earth). After making a copy of that recording, Burtt realized that when he slowed it down and stretched it out, he ended up with a sound similar to the rocket one in the PBS documentary.
But it wasn't quite right, so Burtt took the sound of the elephant and mixed it with pass-bys he'd recorded of cars during a rainstorm as they sped through puddles in front of a motel where he was staying (a pass-by is when a vehicle comes toward the viewer, passes by, and then speeds away).
"Swoosh, the car would come by, and you heard this car plowing through the water," he says. "I took that sound still thinking that I was making a laser of some kind." The key "a-ha" moment occurred during temp track auditions, as shots started coming in from ILM of the gunport sequence.
"When we did temp mixes and played it back for the crew at Park Way, I would take advantage of the fresh audience, because the editors hadn't heard anything with sound," Burtt explains.
"The gunport sequence came along with the first trial shots of actual TIEs in motion. There was pressure to just get some temporary sound in for a screening, so I grabbed a random set of sounds I liked and cut in a different one each time a TIE fighter zoomed by," continues Burtt. "One sound was the elephant shriek, the next one was a slowed-down World War II warbird, the next a processed jet or rocket."
After the screening was over, the only talk in the room was about that elephant swoosh sound. "That was the greatest sound for those ships you could have possibly picked!" Of course, I was saying, "Oh yeah, of course". I’d really put it in because I had no other altemative, but it got great reviews, so naturally it became the sound of the TIE fighters."
"In World War II, the Stuka dive-bombers had an artificially created siren wail created by air ducts," explains Joe Johnston, visual effects art director. "They didn't serve any purpose except to create this noise, which would terrify people. It was intended that the TIE should achieve the same effect."