It is difficult to give an authoritative answer because who knows what a "typical" pie might be like. It might be different for every person you talk to. I will therefore answer just for myself.
All of the made-from-scratch pudding pies that I have made have been very similar- a lot of sugar and fat and some starch to make the gel. Usually recipes also call for egg yolks which also help with binding but make the pudding a little more custardy instead of just a gel.
The texture should be sliceable so that the sliced edges sag but don't flow. I have had pies that have to be scooped out which, while perfectly delicious, isn't as nice a presentation. On the other side of the spectrum is what you have- rubber- which is a great presentation when cutting but not much fun to eat.
Gradually adding your corn starch slurry is always a good idea. Often the starch is mixed with the sugar to make sure it is evenly dispersed and then added to the liquid. As long as you didn't have clumps your technique here was fine.
I don't think your expectations of a banana pudding pie or your technique are wrong. What I think is slightly wrong is your expectations for this recipe. It's "wrong" to call something a "take on a southern classic" that uses soy milk and organic margarine. The milk fat and egg yolks in typical recipes do a lot to make a smooth, custardy pudding. Doing this with different fats and soy milk could be good but I would expect it to be different.
The bananas don't have to be precooked- that would be horrible, I haven't used earth balance but if it behaves like normal margarine then your crust sounds like it is pretty normal. The number of bananas also sounds reasonable. You want a good layer but not so much that the pudding can't work in to bind it together.
Reducing the amount of corn starch a little should make the filling softer and more to your liking. You could try adding a little more fat which will also soften the pie. In the end though, I wouldn't expect a typical texture of a pie that is made completely of non-typical ingredients.
Well, no one else has answered, so I will. I made the pudding again, this time I did the "dump" just as the milk and syrup started climbing the sides of the pan. Apparently the tiny temperature difference between that and "almost boiling over" was the difference. The second pudding was completely smooth. The recipe is great and it works just like ATK promises. Now I need to find that chalazae removal tool SAJ showed me!
Best Answer
If you are interested in food safety alone, there is no problem. You might get a bit of a "starchy" or "floury" taste, but not necessarily so. The main ingredients are some kind of starch, sugar or other sweeteners, flavour and possibly some additives. None would pose a problem if eaten raw.
But the real issue is that the texture of your dessert may be off:
The main ingredient in an old-fashioned pudding mix is starch. That starch needs to be heated to gelatinize or, in other words, to thicken the liquid. To achieve good gelatinization, you need to boil the starch for a few minutes. For instant pudding, the starch is pre-treated and often other thickeners are included, so you can skip the cooking step.
Depending in the recipe, using the type of pudding that needs to be cooked instead of instant, will likely result in a more liquid or soft dish. As you don't give the recipe you used, it's hard to say, how much it depends on the pudding for consistency, so you could end up with anything between a total failure and perfectly fine.