What is a PCIe slot with an "x4 slot" and "x16 connector"?
Your assumption is correct. This would be a slot with only four PCIe lanes connected, but it can fit a 16-lane card.
This is pretty common, as PCIe devices are meant to be able to negotiate their connections and use lower bandwidth (usually at the cost of performance) when that's all that's on offer.
This is not always true though - I have seen some graphics cards and one RAID controller in my time that refused to work in anything but their full designation (x8). But I've also seen hundreds of devices that were fine. So your mileage may vary on success.