Absolutely

As another answer points out, smiths of the past knew how to make "good steel". They had no idea why it worked, or that what was really happening was alloying carbon with the steel, because the atom hadn't been discovered yet, never mind identifying "carbon" and "iron" as independent chemical elements. All the same they were able to work out procedures to reliably produce good steel.

For a more recent example, consider antidepressants. Evidence is pretty good that they work (even if exactly how well is up for debate). But we don't really know why they work. We have a good idea what the effects of taking them are, generally. But we don't even know which of those effects are therapeutic & which are a side effect, never mind how the therapeutic effects actually fix the problem.

In general, it's easier to prove some device works, than to explain how it works. Proving it works is just a matter of running a few well-designed studies - keeping notes, and crunching some numbers, basically. Explaining how it works might require principles we don't even know exist.

Thought experiment: Time traveller gives X-rays to the 1200's

Imagine giving someone from the 1200's an extremely detailed instruction manual, outlining step by step how to construct an X-ray machine (the medical device) completely from scratch using period-appropriate technology.

It explains everything they have to do, from how to build the tools they'll need to have in order to build the better tools needed to actually make the thing, to how get & refine the raw materials, to operating the device & developing the pictures. But not one word about any underlying theory.

They won't have any idea how any of it works. Physics hasn't even been invented yet, never mind nuclear radiation. But they can easily able see it does, in fact, work - they x-ray a subject, they can see the bones, and can easily verify they really are seeing them by (for example) breaking some bones of a pig carcass.