The answer to your questions depends on how much oil is used and how it is used.
When oil is used in the dough itself, it increases the extensibility (stretchiness) of the dough by coating the gluten strands so that they glide over each other more easily. If used in sufficient quantity, it also contributes to the tenderness and softness of the finished crust and crumb by retaining more moisture and gasses in the dough during baking. If you are also using sugar in the dough, which many people do, it also contributes to the tenderness of the crust and crumb. So, if tenderness in the crust is desired, a good way to achieve it is to use both oil and sugar. Usually, oil will materially contribute to the tenderness of the crust and crumb only when used at fairly high levels, typically around 6-7% (by weight of flour).
Of course, oil provides flavor to the crust, especially stronger tasting oils like extra virgin olive oil. The oil also provides a “fat” mouthfeel, which appeals to many palates. If too much oil is used in the dough, it will have the effect of overly “shortening” the gluten strands. This will result in a more biscuit-y or flaky crust. That is why deep-dish doughs use anywhere from about 7% to over 20% oil in the dough. Even doughs intended to be used to make crispy, cracker-style crusts benefit from fairly high amounts of oil, but usually below 7%.
Oil also has superior heat transfer characteristics. That is why you will get a nice, crispy “fried” effect when you place oil in a pan (a well-seasoned or dark anodized pan) before placing the dough in the pan and baking the pizza. Similarly, if you coat the rim of a pizza before baking, the oil will promote top crust browning, again because of its favorable heat transfer characteristics. If oil is placed on the dough before saucing, which some pizza operators do in advance of an anticipated large volume of orders, the oil, which has hydrophobic qualities (it repels water), will prevent or impede migration of the sauce into the dough so that no gum line forms. The oil on the dough also captures and retains flavors produced on the pizza during baking by the cheeses and toppings.
As you can see, oil serves many roles, and I wanted you to see them all since oil is a major component of many pizza doughs, and how you use it and in what quantities can have a material effect on the finished crust and pizza. In your case, against the above backdrop, your use of oil will have modest effect on your dough and crust. If you are using four tablespoons of oil for 2000 grams of flour, that comes to about 2.7% (by weight of flour). Reducing the amount of oil, or eliminating it entirely, will lead to a somewhat crispier crust, but it will also be a harder crust, much like the classic NY style crusts that use little or no oil in the dough. If you are like me, you are likely to notice the absence or reduction of oil, in terms of taste, crust texture and mouthfeel. If you reduce or eliminate the oil entirely, you are also likely to experience reduced crust browning (unless you have ample amounts of sugar in the dough). The reduced browning will be most noticeable in low-protein flours because there is less denaturing of the protein during baking.
You didn’t indicate what style of pizza you are making, so I have assumed that you are making a style other than deep-dish or cracker style. But if it is a cracker style pizza, you will want to have some oil in the dough, as pointed out above.