Yes, you will get more curds. Producers in markets with low legal requirements on labeling and high price sensitivity (e.g. Eastern Europe about 10 years ago) used to do this a lot for feta-type cheese. They still do it, but nowadays they are required to label the cheeses containing vegetable fats, so their more expensive competitors producing standard cheese have part of the market too.
When you use vegetable fat, you get more curds, and a very cheese-like taste, at least if you do it properly. (I suspect that the producers emulsifiy the fat first, but have no detailed knowledge of their process). Under some legislations, you cannot call the product cheese, but this will vary regionally, and probably won't matter to your kitchen.
As for the proteins, you probably want them to be in a curdable state before you add them. If you add proteins which have already been curdled and then pulverized, they will just get in the way of the existing ones and create a cheese with a bad texture. I think that the typical whey protein isolate you can buy in a sports store is already curdled, but my experience with it isn't very extensive, maybe there are curdled and raw products on the market. What you can use is to e.g. add fresh soy milk, in which case you will be making a hybrid of cheese and tofu. You could use milk proteins, which will give you a good cheese, but I am not sure where you can find pure milk proteins as opposed to normal powdered milk which still contains the fat and carbs of the original.
As for the taste and texture, they will be far from normal cheese. Without the benefit of a research lab and food technologists working for you, you are unlikely to create a good imitate tastewise. Even the commercially produced vegetable-fat-feta has some difference from pure-milk-feta if one knows what to look for, and its melting behavior is totally different from normal feta (it practically dissolves). So, I don't know why you are trying to do it, but while you certainly can produce some kind of edible result, don't expect to get a perfect cheese imitate.