Find relevant digit groupings
Brachylog, 8 bytes

ḃ₁₀₀₀↰₁ᵐ


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The blackbox function goes on the second line (or the "Footer" on TIO) and the integer is read from STDIN. Prints true. or false. accordingly.

ḃ₁₀₀₀      Compute the base-1000 digits of the input.
     ↰₁ᵐ   Map the blackbox predicate over each digit. We don't care about the
           result of the map, but the predicate must succeed for each digit,
           otherwise the entire map fails.