Input voltage/current required for LM1117 3.3 Power Regulator
Yes, you can power an LM1117 from your power supply.
The droput voltage is 1.2 V so...  1.2 + 3.3 = 4.5 V ....you have 0.5 V headroom. 

It will NOT provide 800mA at 3.3 V since this is a linear regulator, Iout = Isupply.
You will be able to get a maximum of 300 mA since that is what your power supply is rated at.