Well,
the answer is surely yes. Although you will have challenges, I will say that the most successful
gardening I've ever done has been in containers. It was on a patio in Indiana. Not sure what it is about Indiana but everything grew like gangbusters there.
You aren't going to have a lot of the benefits of planting in the ground, but I'd imagine you'll have fewer pest problems. I think the key to this venture is going to be
compost. In your shoes I would investigate a porch-friendly composter, or better yet vermicomposting which could be contained under the sink. I'm not sure if the
Ruth Stout method works in containers but it's worth looking into. The idea is to funnel all of your organic waste into the containers.
Containers are nice because you can move them. Rotate plants into the best light, take them indoors when there is a frost. It's nice to have a portable garden.
Be sure to have pollinator-friendly plants, marigolds, etc. Maybe a carpenter bee house or two.
There is a series of "merit badges" in the works here called
Permaculture Experience for Apartments. It's not ready yet but you could read through that and get ideas.