No... but you can get it to set the title of the card. That's the only field you can have it write to. I tried to do this also, and found out that the typeform response just gets saved as a pointer really to typeforms system (instead of writing the values into Trello).
have you tried with Zapier? You can create a trigger when a Typeform response is submitted and next step in the Zap could be fulfilling the Trello Custom Fields. Trello Custom Fields should be created in your board before creating the Zap, otherwise they will not appear when mapping.
Hope it helps! If you guys need a hand with this just let me know!
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