Forget about RPM. The first issue is a simple energy balance. You need to determine the steady state energy requirements of whatever you are planning to power with the system. If the TeeVee requires 150 watts, then you must supply more than 150 watts while the TeeVee is operating or your battery will run down. If the computer draws 200 watts average, then, again, you must supply more than 200 watts to the system.
Keep in mind that you have specified several pieces of equipment between you and the appliance. Each of these, the alternator, the battery, and the inverter, have losses of their own. The alternator is probably the most efficient, but the battery and inverter are probably not very good. I would not be surprised if there were 25% loss in the chain. So a 200 watt appliance would require you to push 250 watts.
However, there is another catch. If the battery starts to discharge because of peak loads or if you cannot keep up with the demand, it will start sucking down power as well adding to your load. This could become a vicious cycle where it gets harder and harder to pedal as the battery become more and more discharged.
Depending on what you want to operate, and how strong you are, it might be feasible.