Does reducing the resolution reduce the used sensor size?

I apologize for my ignorance as I am just a point and shoot camera user wanting some better hardware and was hoping people here could help answer some questions for me. I'm considering buying the Sony RX100 as I absolutely hate how grainy my pictures can be with my current canon pocket cameras with their 1/2.3 sensors (currently using a Canon ELPH 300 HS). The RX100 has a 1 inch sensor, which is fantastic for a pocket camera as a certain review on this site told me...

Here's the question: The 20MP image size seems excessive for my needs. Is there any harm in reducing that to a lower setting? It seems like some people are saying that if you reduce the resolution then you reduce what portion of the sensor is used - is that true? I don't want to reduce to a, for example, 5MP size and then have the same sort of grainy/noise and poor indoor performance I have now. Ideally a camera would use the entire sensor no matter what size of the image I selected but I really don't know and it seems kind of hard to search for this.

I'd love it if anyone could help me out. Thanks.