Ahhh...this could be the case, too. (There's that mandatory 0.3%!) This is a problem that plagued the early 2000's, but most modern hardware is free from it today. If that's what it is, it's not really a "problem" (it won't break anything), but it is annoying. Technically, it's also due to a manufacturing defect. You should be able to argue for a replacement part, since your system is so new. In the end, after spending
hundreds of dollars on a high-end card, that should not be happening. The only thing you should be dealing with is amazing performance.
However, it's still possible it's the fan, as an imbalance in the fans can start as a whine or hum (like you're hearing), then slowly degrade to a rattle over time as the parts fall more and more out of alignment. The noise may also occur only at certain RPMs, not necessarily across the board. So you might hear it only within the "middle range" of fan speeds. Do you hear this noise constantly, or does it come and go during a play session? (Constantly would argue for coil whine, as you suggest.)
In the end, there's nothing else to be done about it except bring it into the shop and have them actually investigate it.
No worries about playing on the system in the meantime, though! Whether it's fans or coil whine, it's just annoying noise, not a sign that anything is damaged. Coil whine is simply micro-vibrations caused by power draw for a part that's not 100% firmly seated on the board. It takes nothing but fractions of a millimeter to cause the issue, and it's normally harmless. I seriously doubt that anything is "broken", but since it's odd for this to be happening on such a high-end part...better safe than sorry. Besides, I'll say again, for what you must have paid for that system -- there should be absolutely 0 issues.