What if I try to connect a 12V@0.16A computer case fan to my USB port?
The good thing is, trying a 12v fan in there should not harm your computer in any way, it just won't be likely to start.

As it says in the question you linked to, most 12v fans will not start up with 5v - they require a higher voltage to overcome initial friction. This is why they say 12v. If you get yourself a 5v fan, with a current requirement below the limits of your USB port you will be able to run it.

In response to your queries re current draw:

USB devices may draw up to 100 mA before "negotiation" with the host, after which they may draw up to what the host gives them permission to draw, which is limited to 500 mA due to physical interface requirements (USB cables, connectors, etc are designed for no more than 500 mA)