Not until the prices come down. Lithium is the cream of the crop in battery technology—so, it’s very expensive. You can’t operate a car with anything else, but there are many other options in batteries for home use. All of them are cheaper. So, at this point, you need really good reasons to use lithium at all.
The goal of the Tesla Megafactory is to flood the battery market in order to bring down prices. If this works, then these batteries may become a good option.
The price of solar itself is largely independent for batteries. Most systems don’t need any batteries, because they are connected to the grid, using it as a de-facto battery (look up net metering). Batteries are only added when necessary, such as in an off-grid situation.
The hope is that prices for all the equipment will come down enough to make it economically feasible for homes to be self sufficient, not needing to connect to the grid at all. We are not quite to that point, although there are a lot of people eagerly waiting (some even paying for the opportunity, even though it may not make financial sense) to be free from utility power.