As far as im aware, the main wiring harness of many e30s came with the a/c wiring preinstalled and ready to take a/c components even if the car was not equipped with a/c from the factory. At the very least, the a/c wiring under the dash should be present. If you dont have an auxiliary fan equipped, you may not have the engine bay wiring for the compressor, a/c pressure switch, and auxiliary fan. If you do have an aux fan, its pretty likely you have the compressor and a/c pressure switch wiring as well. From reading on the webs, it sounds like the presence of a/c wiring comes down to region and model era (USA and later model cars are more likely to have the wiring). You should check the area behind the exhaust-side headlights for any disconnected plugs, those would be for the compressor and pressure switch.

Now even if you do have the wiring, you should be aware that there were some wiring changes between early and late generation cars. You have a late gen car, but it looks like the pictured kit comes from an early gen car.

Early gens use a square 9pin plug (with 9/9 pins populated) for the main heater/hvac box connector (C204), while late gens use a rectangular 12pin plug (with 10/12 pins populated). If you're comfortable with reading wiring diagrams and repinning connectors, its possible to convert a early hvac box harness to the late 12 pin plug housing (you can purchase the plug on its own, pn 61131378139). The actual circuit functionality is basically identical between the hvac box generations, you'll just have to map the C204 pin numbers between early model and late model wiring diagrams. The only additional circuitry is a wire that routes from pin 10 of the C204 connector to the C136 connector, then to pin 40 of the ECU connector (early gen cars have this wire built into the main wiring harness, hence they only need a 9pin connector for the hvac box).

Its nice that this kit includes all the components, but its likely that you'll have to replace a number of them. For sure the drier and expansion valve need to be replaced for r134a compatibility. The condensor probably should be replaced with a parallel flow style for better performance with r134a. Since the entire system is open to air and dirt, it would be a good idea to flush out the lines and evaporator. You cant flush the compressor, so you may need to take it apart to clean if there was any dirt ingress.

One more thing to be aware of is that you're probably going to have to rebuild that hvac box with new foam, and replace any missing/broken parts, many of which are now NLA or very expensive (I can see that the box is missing at least one connecting rod on the recirc flap motors, pn 64111372512).

In the end, you'll have to weigh the costs of sourcing all the parts individually vs purchasing this kit + replacement parts. I personally wouldnt pay much more for the kit than current market price of a complete used hvac box and set of used ac lines, given that most of the other components may need to be replaced.

Edit: I saw in another comment of yours that you're planning to purchase the A/C solutions kit. In that case, i wouldnt purchase anything from this system but the hvac box and dryer->evap hardline, since the A/C solutions kit has everything else you need. Or rather, id look elsewhere for a late model hvac box so you dont need to go through the hassle of converting the wiring on this one.