Definitely a big no no.
First you have to consider the efficiency of PSU, most normal PSU
have only an efficiency rating if around 60-70% of the rated, so
how much real power you are getting off the 12V rails maybe only
300+ Watts.Even High end PSU like Seasonic ones are in the 80+%
region.
Then you have the rest of the system to power too.It may work when
you just running normal applications, however when you are gaming,
the PSU may be overloaded.Then Pfft, it may blow and fry other
components like motherboards.