Would it be ok to run a 1 farad (1000 watt) capacitor to a 1600 watt amp? will it blow... (or something lol)?

NO it will not blow but it is too small to benefit you very much. Are you talking about 1600 watts peek or RMS? If it is 1600 watts peek you are drawing up to about 130 amps, if it is RMS you are drawing about 200 amps. Either way it is too small. One thing to remember is that Capacitors are most beneficial when the car is running. They release stored energy when the vehicles charging systems potential drops below the potential of the energy stored in the Cap. Caps only help during the brief moment when the b hits and the amp draws more current than the battery and alternator can provide. If you continuously use more current than is available the cap will not be able to "fill" and becomes useless. Adding a battery or upgrading the alternator are the only thing that will help. Alts are only beneficial when the car is running. Batteries are the only thing that help when the car is off. If you have not upgraded you "big 3" you are going to need to.