Not typically, but it depends how bad they are. They introduce too much air into the engine, which makes it run lean and hotter.
What you say is sort of right, but practically speaking not really right either.
The car uses the O2 sensors to check if the combustion is right, so it will simply just add more fuel into the cylinder as necessary.
If the short term fuel trims and the long term fuel trims go above their maximum allowed values (25% or so on the explorer for the long term fuel trim) it throws on the Check engine light and starts doing some other "weird" stuff. But sadly I forgot what exactly it was. I think it goes into some safe mode and then uses the third (or third and fourth if you have a fourth) O2 sensor(s) downstream behind the catalytic converter for the engine management, or something like that.
That's obviously done this way so that it doesn't just totally unreasonably keep adding more and more and more and more fuel, which at some point of course would obviously be really bad.
So yes, vacuum leaks do affect the MPG negatively. But they don't just do it in an all simple manner, because the combustion is always monitored and optimized via the O2 sensors and the PCM adjusts for the extra air.
When the vacuum leak is big enough though (and it doesn't take much of a leak to be "big" enough) so that the PCM runs the engine outside of the proper operating parameters, that's when the engine REALLY starts running "wrong" or "bad", meaning most likely lean or whatever else the PCM programming might make it do then.
I'm writing it this way, because for one, as I said I'm not sure how our 2nd gen. Explorers PCMs react then, and because there are also a bunch of other examples of "modern" cars like my dad's Audi A8 for example, that will then just go into sort of a "failsafe" mode to protect the engine and ( in this case more importantly) to protect the (really awfully expensive) catalytic converters and will then only let you drive the car slower than about 35 MPH in order to get it to a dealer or garage and have it fixed (and pay a bunch of money).
P.S.: If you don't need to pass emissions tests and don't care much about pollution then you might of course not worry much about your catalytic converter. But if you have an older car and you live in Germany, or generally in Europe, or any other country that actually does have mandatory emissions tests where they do really measure and check if the catalytic converters operate and function according to the regulations before letting the vehicle back on the road - THEN you would definitely worry a lot more about your "valuable" catalytic converters.
Whenever I had to get rid of an old car in Germany for example, it was mostly because of them failing biannual emissions tests and usually not them failing the technical safety inspections part of the check. And that is simply a) because my cars were and still are always technically safe and b) because it's AWFULLY EXPENSIVE to replace a catalytic converter with a new one if the car fails the emissions test. Replacing a catalytic converter can easily cost more than an old cheap car is worth.
