You may or may not have noticed that this recorder site is practically dead as nobody bothers to respond to questions (much less respond to answers) anymore. You’d have much better luck on FaceBook on the following pages: The Recorder Cafe, Recorder Players n Enthusiasts, Flute a Bec, etc.
But to answer your question, yes you should both oil the recorders (even if they have been wax impregnated, just to be on the safe side) and most assuredly break them in carefully so they don’t crack. Anti-condense maybe, maybe not depending on if they clog too easily.