Soak breather in oil?

Soaked in oil? No. A bit of oil drizzled into the holes and the cap left upside-down for a few minutes for the oil to coat the filter element, yes.

An empty breather cap: also no, it means dirt gets drawn into the engine every second it's running. Replace that past-due breather.
Mine doesn’t have all the holes at the bottom so I’m thinking the air flow is coming from the air filter hose. I see Hotrod Swinger’s oil cap does not have this hose.