It should take a month at best. I know IRL it took Germany just over a month, but a human player can annex Poland in 7 days in vanilla AoD.
This may have been a fluke (I can't remember from previous games). You'd need to run multiple AI-only games to find out how Germany really performs against Poland with CORE. If this is the real result, perhaps the AI balancing in CORE sacrifices some realism in Fall Weiss for other benefits elsewhere. You'd have to ask the CORE team.
My patrol bomber fiasco - I assumed this was what did the sinking, as it was present in the area and the "sunk by" column for HMS Eagle was blank. I couldn't think of anything else that could be responsible. Maybe I'm missing something though?