Importance of meteorite impact craters in geology?
Impact diamonds

Yes, diamonds can form in meteorite impacts. For this several things need to happen:


A meteorite of the correct size and velocity,
The stuff it hits needs to contain carbon.


If you have a meteorite hitting granite or ocean you're not going to get any diamonds. It usually has to hit something that has biogenic carbon (let's say peat, coal, graphite). Even then, the diamonds will form only in a very specific distance from ground zero, because there is a specific relation between pressure and temperature that has to hold. Pressure has to be high enough to stabilise diamonds, it has to be hot enough to break the graphite carbon bonds, but not too hot to destabilise diamond. This is why it also depends on the size and velocity of the meteorite - only some will make these unique conditions happen. A notable case is the Popigai crater in Russia (that has some weird stuff in it). Another case is the stuff found in the peat around the Tunguska event.

However, calling the material that forms "diamond" does not say much about what it's actually like. In some cases, it's not even proper diamond, but rather a carbon polymorph called lonsdaleite, which is some kind of "hexagonal diamond" which has lower hardness than real diamond. Impact diamonds are also usually not pretty, so they're not suitable as gemstones in jewelry. If anything, they're useful as industrial diamonds. The thing is, that making industrial diamonds synthetically is much easier than digging them up from these locations. So, the answer is no. The economical significance of meteorite impact craters in relation to diamond formation is negligible.

Pretty diamonds usually form in Earth's mantle and are brought up to the surface in volcanic eruptions. They are mined from volcanic pipes such as kimberlites, and even though some of them are named like they're impact craters (like the Crater of Diamonds State Park) they are not actually impact craters.

Other stuff

There is one notable occurrence of an impact crater that did cause economic mineralisation of something: the Sudbury Igneous Complex, or the Sudbury Basic, in Canada. In here, a meteorite impact caused melting of the crust and the formation of a nickel deposit. Currently, nickel, copper and some noble metals are mined from there. Even though it has been known for more than 100 years, only in the past 30 years or so the impact origin of it has been fully accepted.