No. If the xfmr steps 120V rms down to 12V rms, then in reverse you must limit the input on the low side winding to just 12V rms. The output will be 120V rms. The current ratings for each winding still apply.
Do not even think about energizing the low side with 120V. The core will saturate, the magnetizing current will be abnormally high, the voltage on the high side will reach dangerous levels, and the xfmr will overheat, as well as insulation possibly breaking down.
What you describe involves lethal shock hazards. If you are not familiar with xfmrs or electric power in general, I'd advise you not to tinker with voltages of this magnitude. Please heed my advice. Best regards.