I recently got a new pair of IEMs (In-ear monitors), and while sound quality is really good, I am getting a constant hissing sound when I use them with my laptop. I know that the static is caused by interference with the on-board audio, but I was wondering if a simple USB to 3.5mm adapter would have any effect on it, or would I have to get a USB sound card?
The “USB to 3.5mm adapter” you link is exactly the same thing as a “USB sound card”. USB is a generic digital protocol; the only way to “adapt” it is to provide the USB-device and digital-to-analog hardware that is commonly called a “USB sound card”.
The remaining question is the quality of the device. I would be wary of a device which calls itself an “adapter” and is notably cheap and small being built low-quality to the point of not being an improvement over your laptop's built-in audio hardware, but that's just speculation based on marketing, not an actual technical fact.
In the end, what you need to know is that the thing you are looking to buy, under whatever name, is the electronic device primarily responsible for the accuracy of the signal going into your headphones, including the absence of the hiss you are concerned about. For this particular problem, the quality of that device is the only thing that matters.