> What will happen is that the local baseline load rises to accommodate the greater supply of power

Maybe. Electric companies used to have policies that encouraged that. Most people are asleep between midnight and 6am, so if you used a lot of electric at that time they would give you a large discount on electric costs. However most people would not get up at 3am to take shower even if it would save $20/month (must be a really high flow shower to save that much). However those policies have changed over time as now the electric company is going to give discounts if you can use power when the sun is bright or the wind blowing (depending on where they get their power).

It will always happen. The baseload doesn't need to be composed of residential buildings. If there's a big glut of power between midnight and 6, and the local community doesn't want it, businesses will appear that consume power between midnight and 6.