Did Gravemind let Cortana escape?

An interesting clip from Halo legends that appears to feature the Gravemind intentionally handing over Cortanas data chip to Chief. While this scene may simply be a weird stylistic choice on the part of the animators, the dialogue that accompanies it makes me think otherwise. Does it suggest that Cortana may have been afflicted by logic plague on some level? There is a parallel between what this scene seems to hint at, and what happens in the aftermath of the Ur-Didacts interaction with the Gravemind in Halo:Silentium, the third novel in the Forerunner trilogy.
The Ur-Didact is not shy about describing how unpleasant his interaction with the Gravemind was, but in the aftermath of that extended interaction the Gravemind merely allows the Ur-Didact to leave his presence without any permanent physical harm. The Ur-Didact returns to his people, but then eventually reveals he has a brand new distorted perception of the mantle and its precepts, and proceeds to argue that the mantle belongs to the Forerunners alone, and that it must be taken and enforced by force. These actions while not actively in support of the Graveminds immediate goals, end up being a huge detriment to the Forerunners own plans. The Ur-Didact proceeds to create the Promethean knights using the composer.
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[@TheUltrafan25]

Even the ending to the cortana mission in halo 3. Gravemind let Master Chief go and helped the pelican get out of high charity.

[@Hazel-rah]

This would be a great plot twist. What if the Gravemind let the Master Chief capture Cortana, because he either absolutely corrupted her, turning her into a sleeper agent of the flood, or it knew that Cortana was so damaged that releasing her would subject the universe to chaos. On the last point, the flood were created to do this, being chaos and destruction to the universe, so perhaps the Gravemind could be playing out a long term plan, as by the end of Halo 5, Cortana had taken over the Guardians, the Prometheans, enlisted an AI army and had control of many forerunner worlds; meaning she was definitely in a powerful place.

[@Hazel-rah]

This could have been a very entertaining and interesting storyline to be followed with Halo 6, but instead we got the pathetic excuse of a game that is called Halo: Infinite. They would not have even needed to include the flood in Halo 6, but there could have been a lead up to it for Halo 7, or a complete scrap on the flood and perhaps something else involving Precursors.