Am I correct in understanding that the card will run at PCIe gen 3 X1 if I do this?

Correct. The situation you described in the original post would result in Gen 3 x1 speeds.

The interface will always default to the fastest standard that both sides can support. If one is gen 2 and the other is gen 4, gen 2 is the highest that can be supported. If one side is x8 and the other is x4, x4 is the highest that can be supported. In this specific case, if you put a Gen 2 x8 in a Gen 4 x1 slot, you will get a Gen 2 x1 link.