I assume you are talking about snow/sugar snap type peas rather than shelling peas? If you are talking about shelling peas then that area isn't near enough.

If you are talking about the edible pod peas then yes, that is enough area for 3 people although you may not have enough to freeze some for use later.

Planting in a 4x4 area may be challenging to harvest from though and I wouldn't expect the plants in the middle of that block to do particularly well due to shading.

Typically what I do with snow peas is make a row about 1' wide by as long as I want it. This spring it was only 4' long. I use stakes about 3' tall and run twine between them as support every 6" or so. For the shorter varieties this is ample.

Harvest is variable. This spring it was ample for a family of 5 for salads and stir fries, but nothing left for freezing.

That all depends.

I grew about a pint( at least. Basically a bulging sandwich bag) a week of snow peas in about 2 and a half square feet with low density as about 6 per square foot. If I did that in 16 at 9 per square foot I would have been buried in them. I had 7 foot vines this year certainly helped by mild weather. Any edible pod pea in 4X4 is plenty of space but you will need more for dwarf types than a few square feet but 16 is plenty. The earlier it is, the smaller vines and the less it will be down the road. As of now in 1 square foot I am producing rattlesnake beans at about two pints a week completely out doing 4 square feet of bush(I use these for early beans and plant to the south because of shade). The variety is a critical factor in yield. Flat Romas are still growing.
As for shell peas 4X4 is certainly a decent crop of peas for a nice little side dish once or twice a week or perhaps more for big vine 5' plus late maturing types. If you want just peas its worth while if not a huge feast.

Thanks.

Yes, talking about peas to shell and eat.

And you are right the middle got shade and poor growth.

How big a space do I need for shell peas for 2 or 3 people?

I planted mine to grow up trellises in rows 2 plants deep, with more shade-loving plants (lettuce and other greens) between the trellises. 8 feet of plants produced about 3 cups of shelled peas.