Yes, I'm afraid that, when these imported Chinese coop say '3-4 birds' it really means a maximum of two. Sadly, many people new to poultry keeping take the specifications as reliable, when you have seen for yourself how small the run is, in relation to the number of birds suggested. Adding another nestbox would not be a good idea, two boxes are fine for 4 hens, and one of the first things you should do when getting new pullets is to train them to roost on the perches, not in the boxes, because otherwise the boxes get filthy and hence the eggs also. (You just have to go down once they've gone to bed, for a few nights, and if necessary lift them on to the perches, they soon get the idea.)
I agree with Chris about ventilation, as well. Chickens need a constant flow of air through the coop, winter and summer. They don't feel the cold, but they need cool, dry air, to prevent condensation and the transmission of bronchial diseases. If your run is really secure you can leave the pophole open all the time, which will help a lot, but you still need ventilators at roof level as well.
If your run is going to be covered, the wood of the coop will last longer than if it's out in the rain, but it will be made of very thin stuff which many people have found to warp and leak after a year or less. If you're going to leave it out in the rain, it will need several coats of wood preservative or creosote, and time allowed for this to dry completely and the fumes to disperse, before the hens go in. At this time of year, this could take a couple of weeks at least.
Sorry to be so gloomy, we don't mean to upset you, but it's perhaps best to find out these things before putting any birds in there. Since you obviously won't be needing the run itself, as you have plans for something MUCH better, I would hold off on getting the birds and see if you can get a refund on the coop/run combo, and spend the money on a more suitable coop for the number you intend to keep. In any case, wait until the new run is completed and safe for them, before they arrive. They need the space and safety of the run they're going to live in, right from the start. Chickens hate change, even moving a coop to the opposite side of a run is a major upset!
Or, of course, with this coop, why not just get two to start with, and see how you get on?