Would these Drag rims fit on my 67 Dodge Dart?

I would not use an adapter plate. Dr.Diff has upgraded axles that use the 5 on 4-1/2 spacing.
I’m not exactly sure how a newer set of axle would work from the same size rear if offered would work.
Generally speaking, *I Think* a back spacing of 4-1/2 inches would be fine. Visit the sticky on wheel and tire combos. That will contain who did what with there wheels and often with Wheel dimensions so it fits really really good.