Yes – but with greatly reduced efficiency. Expect your panels to only produce 10-40% of their rated capacity on an overcast day.
An important thing to keep in mind is that, when considering if solar energy is right for you, you should be looking at how much sunlight your home will get over the course of a year, not on any one particular day.
In fact, many locations around the world with the highest rates of solar installations aren’t known for their abundance of sunshine (Germany, for example).
If it is overcast today our whizbang solar panel forecast tool can show you what you should be getting (approximately).