I can confirm that even a cheap air cooler is more than upto the task for all current Intel cpus because the heat output is lower with the newer generation stuff.
Another plus side is power management on all current hardware greatly reduces heat when a system is doing easy tasks like surfing the internet and whatnot. This means even a slow fan will have no problems with heat.
Now onto the unplug it part. Disconnecting the pump when the system is not working hard(so not playing games or running another heavy task) will not hurt the system(you only need to disconnect it for long enough to hear if the sound goes away.). I recommend this just to be 100% sure the pump is the noise source. Some users have had luck slowing pumps(I do this my self for the all in one on my video card.), but I do not recommend it unless you are keeping an eye on it to make sure it does not stop turning.
As for quiet vs loud, something like the NH D14 could keep an i3 system running well within specs even with a single 600rmp fan. This is because the heatsink is so large. I actually have an H80i on my cpu because my case is very small. The H80i pump makes no noise that can be heard unless you have your ear to the pump it self(and even then it is hard to hear it). The LQ310 on my video card on the other hand is louder than the stock cooler for that video card(this is the reason I slowed it down, it is not silent, but very quiet now.).
When you have the room air coolers are almost always better than these all in ones when you take into consideration the price. The air cooler(aftermarket ones with lots of surface area) can also have a fan fail and still run for a very long time under medium loads without overheating.
I am not knocking the all in one idea, as I do use them when space is a concern.