If there is any historical, rather than intrinsic, connection between the Atouts and the Tree of Life, then it is more likely to be in the various ways in which the letters have been incorporated into the deck, and how (if at all) the letters relate to the Tree.
The Sefer Yetzirah of course makes it clear that the letters are placed in a circle, not on any so-called paths which some Kabalists (from all persuations) seek to place to link the Sefirot.
If the letters are placed in a circle, there is also ground to consider that with these the swirlings of Da'at are formed - ie, the Tree of Knowledge, rather than the Tree of Life.
Both the (Continental based) Ordre Kabalistic de la Rose Croix and the (British based) Hermetic Order of the Golden Dawn have used (different) methods which seek to integrate or concatenate Kabalistic and Tarot considerations - and have done so in differing ways.
Two of the questions which I personally consider are important to consider is what the Tree of Life depicts (in a nutshell, a representation of progressive archetypal creation, emanation and manifestation); and what Tarot depicts (again in a nutshell, a progressive integration and spiritual ascent of the individual). Neither of my bracketed overly succinct 'answers' are of course adequate - but I write them in order to justify what follows.
Like many, I also consider that an ascent upon the Tree depicts the individual's ascent towards the spiritual realms. Likewise Tarot.
If one looks at these in sequence and as wholes, it becomes somewhat incongruous to correlate the Tower with Keter - yet there is also a sense in which every single card can be therein (ie, in Keter) reflected and considered. What and how does Keter become reflected in, and is itself a reflection of, each and every card?
In that sense, certainly the Maison Diev can be seen in Keter, and Keter in La Maison Diev. The Lightning bolt to the side as a representation of the whole Tree prior to its even existence (from the Ain Sof), the apparent progression of falling 'shells', the very fall of Adam from the heights of the Crowned mansion.
Could not the same description be also made of the same card if placed in Hesed? and here the very love of the event, the covenant implied in the divine act, become also apparent. Likewise, if the card is considered from Malkut, one sees how the very tumbling from the heights requires than one stay firmly on the ground... of course, we could each add more to the many considerations about each card in each and every Sefirah.
In my view, it is through indepedent study of the Tarot and the Kabalah that any integration will be discovered - rather than by adopting the correlations preferred by Wescott or others.