It can be a lot of draw - depending. Full sine-wave inverters will draw much more than modified. In standby mode, some of them draw 2.5A with no loads connected. All of them of any useable size will draw at least 1A. One can use load search functions to bring this draw down considerably to ~250 milliamps, but these do not always work
well for particular applications.
For example, any wall-wart chargers left in outlets will trip the search mode into full standby power because their transformers draw power even when nothing is connected. Also, things like a microwave will never activate an inverter in search mode to provide full power because its clock doesn't draw enough to activate the inverter.
Search mode adjustment is a fine-balance act that I have never mastered. I just switch the inverter on and off as needed.