If you asked a 6th grader, she would say no, on the face of it. Because, you know, numbers. But this is a real-world problem with real-world measurements and tolerances. Yes, the inequality is false, but it might not matter. It depends on how the tolerance was determined and how it is being used. If you idealize this then 6.665 inches plus one angstrom is out of tolerance but that no longer makes any sense.
My position, basically, is that any given measurement will give one of three possible results, not two: A measurement can say “This part is in spec”, it can say “This part is out of spec”, or it can say “We don’t know if this part is in spec or not”. The more precise the instrument, the less likely that last answer is: A terrible instrument will always give an answer of “We don’t know”. The closer the actual value is to the edge of the tolerance, the more likely that last answer is: A part that’s right on the line will always give an answer of “We don’t know”.
A part that’s 6.6650002 inches that should be less than 6.665 inches will usually be in the “we don’t know” category. With an extremely precise instrument, it would be in the “known not in spec” category. But never would it be in the “known in spec” category.
A resolution of 0.0001 inches does Not imply an accuracy of 0.0001 inches.
And accuracy of the sort you mention especially with 6+ inches + of measurement is very doubtful unless done with very sophisticated instruments.
For example, see page 11 of 76 of this document for micrometer errors. The maximum reported error is about 117 micrometers (0.005 in). https://www.mitutoyo.com/wp-content/uploads/2013/04/E11003_2_QuickGuide.pdf