Yes and no.
Historically, Karate developed from Chinese kung fu flavours. Thus, it inherited some of the shortcomings and inherent flaws of these styles, as written by Steve. That is only half of the story, though.
On the island of Okinawa, this style of fighting experienced a cultural contextualisation: Firstly, the Okinawans were more readily testing techniques in open bouts and were quite militaristic towards the end of the 19th century when te (later kara-te, which originally probably meant 'Chinese hand' and was reinterpreted later to get rid of the mentioning of anything Chinese) arrived and was more widely trained. This kind of pressure testing and combat application was already in decline in China at the time. Same holds for mainland Japan, which is one of the main reasons for karate's transformation when it spread. Secondly and more importantly, there was traditional Okinawan wrestling called tegumi.
This means two things: Firstly, every young man on Okinawa starting karate knew how to wrestle. They did it through all their childhood. Secondly, while not necessarily part of the curriculum proper, grappling was seen as a given and was systematically integrated into the fighting and expanded upon. That is what most of the currently obscure kata movements are about, after all. This strange move where they end up bent over, low stance, with forearms crossed? That's a sprawl to defend against a takedown.
Thus, you would have to see karate and tegumi as conjoined twins sharing vital organs: only as a unity they are whole, and wherever you feel that there is something lacking in karate, these gaps would very likely have been filled by tegumi in historical Okinawan teaching.
As the more-or-less-accurate post in the link points out, much of this has been lost due to various reasons so that contemporary Karate evolved into something that indeed has inherent flaws in terms of a fighting system.
Does that mean that Machida did not do karate in MMA matches? This depends on the perspective. If you listen to the Lex Friedman podcast with George Saint-Pierre, who came from a kyokushin karate background and was one of the best to take people down and control whether the fight takes place on the ground or standing up, he answers clearly that it was his karate training, not his BJJ or his wrestling training, that enabled him to do this. Karate taught him the distance management and timing necessary for his MMA dominance. Machida often referred to karate being the base of his fighting style in a similar way when asked about this in interviews.
Thus, I'd say karate for itself is no good for MMA and grappling defense. But if two of MMA's all time greats came from a karate background and said that this was the base and core of their fighting style, it certainly can ne appropriated be and augmented or 'made whole again' if we speak in the above picture. This is mainly due to the footwork, speed, and distance management it trains along with solid punching and kicking skills, especially when you train a full-contact style.