Maybe. Depends on the plant. Nearly every plant goes through shutdowns for maintenance. If energy is a large cost they work with the utility (and vice versa - when the utility needs to shut down a big power plant they need industry to shutdown something at the same time). Many of them take December off for maintenance. My company has long pour iron in the foundry only at night: we get enough of a discount on power as to be worth paying the workers extra to work the night shift (I last checked this 15 years ago - I would not be surprised if this has changed now that the local power is mostly wind and thus has different factors)

Of course every plant is different. There is a big difference between "batch" processes where you can shutdown after any batch, and "continuous" processes where startup/shutdown is a large process since the machines depend on running. They have different abilities to respond. Some plants/processes use more energy than others - obviously if they don't use much energy they don't care about free energy much either. The more energy a plant uses the more they are interested in cheap energy. In some cases a less efficient process may suddenly become better when solar is "free"

It's not "will it" it's just a series of balances, capital costs vs energy costs.

If there's enough free energy and automation there gets to be a point where there will be people will start to disregard the capital costs as well and run 0ish input cost businesses with a vertical stack of stuff that they produced with 0ish input cost.