Cal talks about flow in the book. Being in flow doesn’t mean you’re doing Deep Work but if you’re doing Deep Work it probably means you’re in flow.
Having Purpose, Mastery, and Autonomy would certainly make the decision to embark on a Deep Work practice easier, but I don’t think it’s absolutely necessary.
Cal would definitely argue that the practice of Deep Work can help you develop a sense of purpose — not the other way around (see his book So Good They Can’t Ignore You for more info on that).
For that matter, mastery comes from doing Deep Work to build skills in something so I wouldn’t be comfortable saying someone needs to have mastery as a prerequisite to do Deep Work, either.
Autonomy I’ll give you. I would imagine there is something that looks like Deep Work that could happen if somebody was standing over you with a whip and making you do Deep Work, but the psychological component of it wouldn’t be right and I doubt the neural connections that indicate Deep Work is happening would be made.