Some electric and some electronics devices will work fine on a cheap inverter with a bad sinewave, some won't work, and some become severely damaged.
It depends on the type of item and how it was designed, and how clean or dirty the sine wave is. Theres too many variables re the items to power and how clean or dirty an output of the lower cost inverters are, to know in advance if some combination will work.
The only sure way to know in advance is to use an inverter with a very clean sinewave and of course having a Wattage rating greater that the total load it will have to run, and a powerful enough DC supply.
It depends on the type of item and how it was designed, and how clean or dirty the sine wave is. Theres too many variables re the items to power and how clean or dirty an output of the lower cost inverters are, to know in advance if some combination will work.
The only sure way to know in advance is to use an inverter with a very clean sinewave and of course having a Wattage rating greater that the total load it will have to run, and a powerful enough DC supply.