I think heat sinks are more important than cooling fan for most applications.
If you are planning to overclock then a fan would come in very handy (to go with the heat sinks)
You could run the fan at 3v (which is what I do) to keep the noise down, because the 5v fans from China
are actually pretty noisy when running from 5v, at 3v its a lot more tolerable.
Tests run when using a fan showed the temp would drop by around 10-12 deg C
This was tested using the internal Pi measurement tools.
The short answer is yes you can use it without a cooling fan.
Having said that, there is a surpring amount of complexity around the topic. If the Pi starts to overheat it will slow down on its own. Overheating is a function of air flow, whether there is an enclosure or hat, how hard it is having to work, etc. There are some good posts on the subject on Element14, eg Raspberry Pi 3 Cooling / Heat Sink Ideas