What occurs if medical insurance 'doesn't cowl' one thing earlier than I've hit my deductible?

From HealthCare.gov (emphasis added):

Deductible

The amount you pay for covered health care services before your
insurance plan starts to pay. With a $2,000 deductible, for example,
you pay the first $2,000 of covered services yourself.

So expenses that are not covered by your health insurance do not get applied toward your deductible (or your out-of-pocket maximum).