I have owned and shot various J Frames for many years.
I would say YES. If, as some others have said, you can shoot it well.
Preference would be a steel J Frame. Not the airweights. Especially for home defense. I recommend not using anything about 38+P (if you have a 357 J Frame) because it'll protect more of your hearing.
With that said, when I've heard a "bump in the night", I've grabbed my J Frame, a rifle, a shotgun, whatever I had handy at the quickest moment and felt secure. With a shotgun, I always had 00 Buck.
I feel a shotgun is ideal. It's easy to work under stress, doesn't penetrate like a 5.56/223 may through your house, and would be less likely to mess up under stress. A revolver of any kind would be second to that.
Adding a 4 inch 357 Mag L Frame would be a good addition. Bigger, easier to shoot, especially if half asleep, and you could still shoot 38s.
A gun is always better than NO GUN. Trust me, most people don't want to be shot by a BB gun, led alone a "real gun."
Keep in mind that these home invading rats we see now a days like to often run with 2-3 individuals (sometimes more) these days while trying to rob people.
Generally you shoot one or two, the others will flee.
They often get caught, either dead in the yard or nearby or seeking medical help. Note that anyone who shows up with gunshot wounds (or by their friends doing the "Homie Drop-Off" as it was called when I worked in hopitals) the police are supposed to be notified immediately. This is how many are caught after the fact.
Some general advice concerning home defense...
Just never answer the door, especially at night. This is a common tactic people use to try to force their way into your home, instead of an outright break-in. Often, the ones who do this ARE ARMED. They'll often use a decoy (typically a woman) to ask for help, to get you to open the door, while they're lying in wait.
I simply never answer my door. I don't care if it's the middle of the day. I don't answer my door. If you're not delivering packages, and I am not expecting packages, I WILL NOT answer the door. Even if you are a delivery service, I typically let them drop it and leave, then grab it.
I don't have people come to my home, so I know if I am not expecting packages, I don't want anything from a stranger... this is just the world we are living in. Safety first and always.