On the subject of cooking, someone once told me "If you have too much water in your pot after cooking a dish, just turn up the heat and let it boil without a lid for a few minutes".
That acquaintance was absolutely correct. There are a number of ways to cheat and quickly thicken a sauce, but (a) this is cheating, and (b) the sauce doesn't taste as good. Reducing the sauce is what the best cooks do.
Knowing when and when not to (and how and how not to) use a lid is Cooking 101. Presumably you can cook rice. You would never cook rice without a lid, would you? (Actually, you can cook rice without a lid, but this is beyond Cooking 101.)
Knowing how to properly reduce a sauce is just a bit beyond Cooking 101. Basically, you turn the heat up and you stir. Stir frequently.
So by that reasoning it seems that it doesn't matter. Or does it?
By way of analogy, suppose you go to a hotel or visit a friend in the far north that seems to think 60 Fahrenheit (15 Celsius) makes for a nice comfy sleeping temperature. Are you going to use a blanket, or say that it doesn't matter and sleep commando? Or does it? That's a rhetorical question. Of course it matters.
It matters even more with cooking.
Update
The reason using a lid (or not) matters more with cooking is twofold. I'll look at this in the context of the question raised in the title of the thread,
Does placing a lid on a pot affect the rate of boiling?
Note well: This is the wrong question with regard to the body of the question. I'll get to that later. The answer to the question raised in the title of the question is "yes".
Some of the answers have posited that the lid raises the boiling point. This effect is marginal. The Clausius-Clapeyron equation describes the relation between pressure, temperature, and the vaporization pressure of a liquid:
$$\frac{d\ln p}{dT} = \frac {\Delta H_\text{vap}}{RT^2}$$
At sea level, water boils at 373.15 K and has a heat of evaporation of 40.657 kJ/mole at that temperature. Linearizing the Clausius-Clapeyron equation yields a 0.2848 kelvin increase in the boiling point for each one percent increase in pressure. Unless one is using a lid that is held down with clamps, this is a small effect. A hefty lid might raise the pressure inside the pot by a few fractions of a percent. This is at best a small secondary effect of using a lid.
The primary effects of using a lid are to drastically reduce convective heat transfer from the steam/vapor to the atmosphere and to drastically reduce vaporization of the water. All other things being equal (same pot, same heat setting, same amount of water), a boiling pot of water covered with a lid will have a higher boiling rate than will an uncovered boiling pot of water. Some of the heat supplied to the uncovered pot goes toward countering the increased heat transfer rate due to vaporization and convection.
You can see this effect if you have pots with glass lids. Cover the pot, bring some water to a vigorous boil, and take the lid off. The boiling rate will decrease once the lid is removed. If you reduce the heat to a low simmer before taking the lid off the effect is even more dramatic: The water stops boiling. Yet another way to see these effects is to time how long it takes for a covered versus uncovered pot of water to come to a boil.
I mentioned above that this is the wrong question. The advice given to the questioner was not about the boiling rate. It was about increasing the evaporation rate for a dish that has a bit of excess liquid at the end of cooking. Presumably the advice was for a dish cooked at a low simmer. Very little water vapor escapes the pot or pan while covered. Most of the water vapor created by simmering instead condenses on the inside of the lid and soon rejoins the dish. The gas underneath the lid is mostly water vapor at close to the boiling point. There is very little evaporation from the food.
Removing the lid exposes the cooking food to air at a much lower absolute humidity. The entire surface evaporates, and the vapor is quickly carried away. Assuming no change in the temperature control, the rate at which water escapes increases significantly even though the boiling rate has decreased.
Note that the exact same advice given to the questioner was given here at the cooking stackexchange site.