No on the s54 housing there is also a bottom feed. But the s54 already has a cooler output so there is no need.
I've seen these caps for s50/s52 housings, but I havent seen the housing itself, so I cant verify if they work.
As you already have the cap, you might test it though (if you get the centerpipe in).
there is oil coming from the centerpipe as well like we talked about (in the normal cap it gets dispersed at the dome). And the filter has a flow resistance. So there still might be oil going through the cooler. Maybe not as much (or better said: all of it), but if you run the eninge and the cooler gets hot, it'll cool.