Mayyyybe. There's a noticeable difference between the two sounds. The Trek torpedo sound has a sharper attack (beginning) and is more resonant. The Martian plasma bolt effect sounds more muffled to me. I suppose it's possible that they're the same recording processed in two different ways, or maybe two different takes from the same recording session, but they're not exactly identical. (Ben Burtt later used much the same process, striking a taut metal cable, to create blaster sounds for Star Wars.)
However, the whistling sound of the Martian War Machines' levitation beams is the same sound effect as the phasers, but slowed down to a lower pitch. And I'm pretty sure I recall the "zee-zee-zeew" sound of the Martian heat ray showing up in ST:TAS. It was definitely used often in Filmation shows.
