No!
Maybe…
Yes?
It depends on what you mean really.
First, Aikido is not a static thing. It evolved over time due to Ueshiba's own interpretation, ageing body, and mysticism evolution. Clearly the Aikido of Hell Dojo was utterly different from the one practices in Iwama: decades separate the two, and Ueshiba moved from a fit young man to an old one.
Thus, a specific Aikido could be understood just fine at certain points by certain students. I think that this matches the three understands_explanations(X, Y, t)
assertions. Clearly, it is difficult to judge unless we can ask any of the students and Ueshiba -- unless necromancy is involved, we can definitely say that this is impossible.
However, there is a method by which we can judge that: Tomiki was given a Meyko Kaiden (later translated to 8th dan) which in the shu-ha-ri (守破離) concept is the equivalent of saying "go away and do your own things, I have nothing to teach you any more". Thus, Tomiki could be said to have been the first person beside Ueshiba to grok Hell Dojo Aikido. Ueshiba told him so by giving him the Meyko Kaiden. Of course, the same could be said of Shioda, Tohei, and countless others too numerous to mention here. Basically, any time Ueshiba gave an 8th dan to a student of his.
Second, Ueshiba was notoriously terrible at explaining things. He would practice a technique a few times, ask his students to do the same, then yell at them when they got it wrong. Even the Aikikai has stories of Ueshiba coming to visit from Iwama and being asked politely (view his wife!) to leave as he was telling everyone they were a disgrace. Was it because he was insane or because he just did not know how to teach is open to debate. If the former, then Aikido was never a static thing in his own head. If the latter, then no one ever grok it at.
Lastly, no one should care about Ueshiba's Aikido unless they are Ueshiba. Aikido of the same style and tough correctly will look utterly different on a 150cm lithe women and a 230cm quarter a ton bench pressing giant. A truly skilled instructor will teach the same technique so that both can make it work. This will become two techniques, both different from the one that works for the instructor. There is no point in understanding someone else's Aikido as it will be utterly useless to you. Understanding your Aikido should be your goal.
As to the splintering of the art, it is another vast topic. However, differences in understanding and Aikido evolutions can explain a lot of it. Adding some massive egos and desire to be the "one true path from Ueshiba" and you get the unhealthy attitude of some Aikidoka. Way of harmony indeed⸮1
1: in case ⸮ does not show for you, it is the irony mark…
2: Thanks to Mark C. Wallace for reminding me of this concept in his answer.