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The rules to the Turing Machine say that none of the verifiers can be redundant in a given puzzle.
A number of the verifiers will validate the count of a specific number in the code. So Verifier 10 validates the number of 1s as 0,1,2 or 3.
Do I understand this correctly to mean that there can never be a positive answer to a count of 3 from a verifier like this, as it would make all the other verifiers redundant by confirming to code in a single test?
You are correct. The problems are set up so that all of the verifiers are required to determine the solution uniquely, and so if one of the verifiers has the condition "There are 3 1s in the solution" it would render all of the others redundant to finding the solution.
This is hinted at in the rules under "Advanced Strategy" where it says:
You will understand, right from setup, that there are certain questions you will not need to ask.
This also extends to interactions between the verifiers - for example, verifier 17 reacts to the number of even digits in the solution, and verifier 18 reacts to whether the sum of digits in the solution is even or odd, which would always be redundant if they were both available.
This could also be relevant in the "Extreme" and "Nightmare" difficulty puzzles mentioned in the rulebook, as a way of ruling out which verifiers are actually active (or which order they appear in) knowing that there are certain ones that should not appear alone or together.
