Yes, it seems so.
Krall explains that the original inhabitants of the planet left behind "technology" for extending life. Having seen the film twice now, I can say that it does seem that his suit contains this technology.
For starters, Krall, Manas and Kalara
were the three survivors of the crashed USS Franklin,
and so Manas and Kalara also needed to extend their lives unnaturally using the alien technology. As you point out, we do not seem them wearing suits exactly like Krall's.
In Kalara's case, almost until the moment of her death she was trying to maintain the cover that she was a scientist with no association to Krall or his drone force, and so she wore a distinct, non-mechanical jumpsuit that reflected this.
In Manas' case, his suit has more in common with Krall's upon further inspection that would seem so at first glance. First of all, Krall's suit has a series of gears located on the shoulders, elbows, wrists, waist, and in some other places. These gears seem to be involved in the life-energy draining process. We see this most clearly when Krall begins to drain Sulu's life energy — the gears go from being inanimate to whirring quickly in unison. I would say this is the best evidence that the suit contains the life extension technology.
You can see some of the gears in this screenshot:
While Manas' suit looks very different from Krall's, it too has the gears: they are simply smaller and fewer in number. One can presume that Kalara, when not in disguise, had a similar suit for her use.
Finally, Krall does age strangely but not unpredictably during the film. In fact, I wouldn't describe the process as "aging". It seems that, when Krall drains lives, he takes on characteristics of that species. Before the arrival of the Enterprise crew, there would have been no humans to drain, and so Krall, Manas, and Kalara eventually took on more and more alien appearances. When he began draining human lives from the Enterprise survivors, Krall
progressively looked more and more human again, albeit with some residual strangeness.