Sure, why not.

I grew them in a 5 gal. container in the Fall. Watch out for aphids. They over-ran my crop.

Also, you may want to give them some support as they can get kind of top heavy.

I'm glad I found this thread because I have one last brussels sprout seedling that won't fit in the garden, but I do have an extra 5 gallon bucket. :)

But for the OP -- am I reading you right that you want to know if you can grow the sprouts in a container on your porch ... with no sun? If that was the question, then that won't work. The plants require full sun. Brussels sprouts are a cool weather vegetable, yes, so you want to time them so they mature in the fall and get a frost or two in before you harvest them. But they take months to grow, so you need to plant them in the garden during the summer months (in that warm and sunny bed) in order to get sprouts in the fall.

Sorry, I missed the "no sun" part. That might be a problem.

Here's a good, detailed article: How to Grow Brussels Sprouts in Containers