Can a cheap transformer be used for twice the rated voltage?
Only for about half a mains cycle.
ie NO. 

Even running a 60 Hz mains transformer on 50 Hz causes it to run hot (ask me how I know) due to increased magnetising current.

Power transformers are designed to use the core iron well (except i very special cases) and magnetising current is arranged to flux the core to the point on the BH curve where the core is starting to saturate and go into a non linear mode where current increases faster than voltage applied or than flux increase.  

Doubling the voltage will drive any normal transformer deep deep deep into saturation, massively increase the current with no positive effects whatsoever, and destroy the transformer almost instantly.