Can a 100Ah battery power my house with my TV being the biggest consumer?
100 Ah at what voltage? Assuming a 12 volt DC battery, it will need to be up-converted to 120 volts – 10 X the voltage, so one amp at 120 volts will require 10 amps at 12 volts to deliver the same power level. That would get you a 10 hour theoretical time – but that voltage needs to be converted from DC to AC, and that will only be maybe 75% efficient, so more likely you will need 13 amps from the 12 volt battery.
Maybe you biggest load will be the TV, but have you considered the refrigerator? In most households that is the single largest user of power, mostly because it is running day and night, every day. There are also clocks and some other devices that may consume bits of power while being turned off, for example any device with a remote control.
Given enough engineering and money, it certainly can be done. To get maximum life from the battery, the battery would need to be designed for deep discharge, something that “normal” batteries are not designed for and they can be damaged by deep discharges. The limiting factor in the design is how much time you demand for the battery life. One would first have to determine all the power required in watts, then select a converter that can handle the wattage, and then select a battery size that would accomplish your desired length of running time. Selecting the capacity of the battery is really the last step in the design of this kind of system. So the short answer is “Maybe it will, maybe it won’t.”