I have run quite a few devices using a modified sine wave inverter. Some like it fine, and some don't like it at all.

Laptop power supplies seem to handle this "garbage power" without a murmur. Most battery chargers put up with it and don't seem to suffer adverse effects over time.

But note that some chargers do not respond well. One of my power tool chargers overheats and shuts down. Others buzz so violently that you are likely shortening their life. Some won't stop charging; perhaps they compare against the accurate line voltage to determine when the job is done. So you have to watch it.

I wouldn't even try to run a desktop PC using an MSW. Macs are said to be particularly averse. And last I checked, some laser printers rely on the accurate timing of grid-based power (60Hz) in their operation.

I haven't tried to run my natural gas furnace using MSW power, even though I can theoretically do so. The control board in these units is worth half the price of the furnace. It's a tricky proposition at best.