It has the pass-through connector specifically so that you can use it. It is just a way to allow you to add the fan without taking up a power connection (useful for PSUs with few connectors). Plugging something into the other connector is the whole point.
It won’t short-circuit the drive or whatever you plug into the other connector unless the fan somehow shorts in itself, but then at that point, everything that is connected to the PSU is at risk (but fortunately PSUs are designed to shutdown as fast as possible when shorted, specifically to prevent damage).
The only real-world problem (as opposed to hypothetical) that you might need to consider is what you are plugging into the other connector. It is rarely an issue, but personally, I like to put my floppy and drives on the same cable as fans and give hard-drives and video-cards their own cable. The fan is unlikely to draw enough power to starve the hard-drive, but if you have a free cable, why not use that for the drive and have something less critical share with the fan?