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A lot of it depends on if the alien technology is understandable under our current physical theories, or if the aliens have discovered some new facet of nature that their tech relies on to work. For example, if we discovered a fusion powered probe, we would know to look for superconducting magnets, and any attached cooling system. If the aliens have some sort of hyperdrive that needs new laws to explain we wouldn't know where to start.
And disabling technology based on new physics could be very dangerous. Imagine if the HMS Astute got dropped in the Thames in 1870, sans crew or manuals. Queen Victoria orders Sir Kelvin to lead a team of Britain's best scientists & engineers to study the strange vessel. Stuff like the steam turbines they would probably figure out easy enough, and be able to make crude duplicates, but when they try to figure out what exactly is boiling the water, well expect a bunch of sickness & deaths before they even figure out it has a bunch of uranium rods. And even after they map out each part & what it is made of, and try to duplicate it as closely as possible, the copy reactor would simply not heat up, since submarine reactors use mostly U235 while natural uranium is mostly U238. Kelvin & his team would have no idea of what went wrong, since the whole concept of elemental isotopes had not been invented yet.
