I have named the members of a group of things in my latest work after the major arcana of Tarot cards. While I can think of a few other works of fiction that do the same thing (the bosses in the House of the Dead series, or the episode titles of Jojo's Bizarre Adventure: Stardust Crusaders), a test reader did not understand the reference and expressed concern that others would not. Is this concern justified?
The first thing you should ask yourself is, will the text be unintelligible without understanding the Major Arcana connotations?
If so, you probably need to add more context for the reader to understand.
If, on the other hand, the Tarot connotation is just semiotic seasoning, and you expected the reader to get the connection, but they didn't and the complaint is that they felt stupid or that you've failed to convey the Tarot-connection, but the text itself and the understanding of it didn't really suffer... then you probably don't have any problems.
I'd even suggest going deeper. The Tarot deck is part of several different systems of symbolism.
Symbols or archetypes, if we're to believe Jungians, are part of our unconscious experience, maybe even inherited (through nature or nurture or both), and as such should still trigger some expectations or understanding even if we don't understand them completely.
First, there are tons of books on what symbolic meanings the different Tarot cards have, and you could probably spend a lifetime digging into it.
If you pick up a copy of "The Living Qabalah" by Will Parfitt, it has an appendix with a table of connections to things like parts of the human body, colors, magical powers/weapons/symbols, precious stones, drugs, perfumes, flowers, animals, etc.
You pretty much get a full set of symbols to choose from.
Take the Fool for instance. It's connected to things like the respiratory organs, air, sky blue color, magical divination, the dagger/fan, topaz, the aspen tree and grasses, eagles/humans/oxen, sylphs, camomile, spruce, Odin, Maat, Maruts, Dionysus, Jupiter/Bacchus, wind, air demons, the Ninth Bull (of the Ten Bulls), the letter A and the number 1.
You can spend a week digging up symbolic qualities for your character from that list and even if people won't get all the connections, it going through your head (filled with Jungian archetypes?) and your choice to include or exclude symbols will likely still make it feel like a symbolic whole.
Of course, if you attach everything to your character they will look like a symbolic Christmas tree and they will probably send off Terry-Pratchettian warning/humor bells. But going deeper with symbols and using them to form your characters, their background, what they look like, how you describe them, etc, will at the least make them well-researched, and probably make them seem symbolically interesting...
Given that the majority of the general public is exposed to Tarot through movies and TV, where the card Death is used to signify literal death rather than its meaning of change, you can expect people to be either uninformed or misinformed.
Roger Zelazny used deck of cards similar to Tarot in his Amber series. While their primary function was communications and travel, the main characters used them like a regular Tarot deck in some scenes. I mainly recall he didn’t go in to explanations or specifics of the cards, but might mention one or two cards at most and without explanation and then the main character would react to the prediction. Zelazny used this for foreshadowing and adding tension.
I think that some readers will and others won't. That said, I think it should be limited to the greater arcana. I couldn't tell you what a three of cups means with a gun to my head.
I would say most people know what the tarot is, and you can use them as cool symbols, motifs, even foreshadowing.
Overall, I wouldn't worry about it to much. It shouldn't be the main focus anyways.