While Ahsoka and Anakin's time together ultimately ends permanently when the former joined the dark side, it's safe to say Yoda picked Skywalker's padawan out for him in Star Wars: The Clone Wars for a reason. Though the two form a somewhat dysfunctional initial dynamic, the padawan and her Jedi mentor quickly forge a strong bond - even if their shared stubbornness often leads to them disregarding the other's advice, ultimately to their own detriment. In fact, the pair's strange but endearing dynamic is arguably one of the highlights of the series - even if it's slightly strange to think that Yoda purposefully put them together.
Yoda appears infrequently in Clone Wars, but it's evident from his appearances that he does have a particular soft spot for each member of this unconventional duo, even going as far as to call Anakin his friend in season 6 - although this was to encourage him to do the Grand Master a favor. With this personal investment in mind, it seems clear that when Yoda assigned Ahsoka to Anakin in the Clone Wars film, he did so with intent - as padawan being actively given to a Jedi by the Council is something that isn't commonly done.
But neither Anakin nor Ahsoka are conventional Jedi, either, as Anakin himself was also assigned to Obi-Wan Kenobi by the council. Indeed, it seems to be that Yoda had seen the Jedi's frustration at feeling as though he wasn't trusted by his peers and would never move up the ranks as a result, and sought to appease these doubts - by providing him with part of the future of the Jedi to train. On a similar note, the book Star Wars: Absolutely Everything You Need to Know also states that Yoda had hoped that "by teaching the Padawan Ahsoka Tano the young Jedi will learn he does not need to be so protective of those who he loves", suggesting the Grand Master was also attempting to help Anakin learn to have some of the detachment that Jedi were encouraged to maintain with their personal lives.
Both elements of the plan end up entirely unsuccessful in the long run, as Anakin's doubts about his fellow Jedi and unceasing desire to protect Padmé at all costs are the two biggest factors that resulted in him becoming Darth Vader. Had external forces not tampered with Yoda's plans, though, it could have well proved successful, as Palpatine's influence on Anakin and Ahsoka's initial expulsion from the Jedi Order - and then her subsequent refusal to return - do drastically change the playing field from what Yoda had likely anticipated. It's clear that Anakin does learn boundaries from teaching Ahsoka, as there are moments where he wishes to defend her and yet lets her learn to fight her own battles and develop in her own right. It's also clear that teaching Ahsoka about many Jedi practices actively lets Anakin feel more like part of the Order - as teaching a padawan is to some degree as much a right of passage for the person training them as much as it is for the padawan themselves.
Ahsoka and Anakin's bond seems fairly tragic in the light of the fact Anakin would inevitably become Darth Vader, but knowing that Yoda saw some shared potential in them and thus trusted Ahsoka to him does show the Jedi Council weren't always an opposing force for the chaotic Skywalker, even if he felt that way. It also paints Yoda in a surprisingly sympathetic light, as his efforts to help both Anakin and Ahsoka would culminate in one leaving the Jedi Order, and the other joining the Sith - which is certainly not the way he likely anticipated things turning out when he created this plan in Star Wars: Clone Wars.