Mostly yes, with two qualifications: waveform and projectors. Modern electronics run fine on decent home inverters at normal listening levels, and plenty of our clients watch through cuts without noticing.
Qualification one is waveform. Pure sine wave inverters produce mains that looks like the grid; square-wave or modified-sine units produce a stepped approximation. Audio equipment, especially anything with a linear power supply such as many stereo amplifiers, can buzz on stepped output, and some switched-mode supplies get warm or unhappy running on it for hours. If your inverter hums audibly through the speakers the moment the mains drops, that is the equipment telling you what it thinks of the waveform. Pure sine is the safe choice for an AV rack, and if you are buying an inverter partly for this purpose it is the specification to insist on.
Qualification two is projectors, and the concern is not running them, it is losing power mid-session. Lamp-based projectors need the cooling fan to run for a while after switch-off; an abrupt cut leaves a hot lamp with no airflow, which shortens lamp life and occasionally ends it. Laser models are more forgiving, but check your manual rather than assuming. A small UPS on the projector alone, sized to give you a proper shutdown rather than a full film, is cheap protection. It does not have to run the show; it only has to let the projector cool down politely.
High-power stereo amplifiers deserve a separate thought. Their peak current draw on a bass-heavy passage can surprise an inverter that was sized for fans, lights and a fridge, and the result is either the inverter tripping or the amp sagging. If you have serious amplification, look at the inverter's real continuous and peak ratings, not the sticker on the front. Loud is expensive in watts.
Where does the rule stop mattering? An AVR with sensible speakers at evening volume, plus a TV, is a modest load and a normal home inverter carries it. Tell us the equipment and inverter model if you want a sanity check before the next cut.
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