Welllll... your instructor knows your local DE's and their quirks better than we do, so definitely talk to him.
But the PTS link I sent you earlier was straight from the horses mouth (FAA) and it's littered with "makes appropriate use of checklist" at every single phase of the flight, from taxi, through takeoff, to cruise, to approach, to landing, and even shut-down. It's literally a line typed into each and every one of those sections.
So yeah... The FAA is a bit checklist crazed, which is not IMHO a Bad Thing(TM) but there are times in the real world where pulling out a checklist would be far less appropriate than having the thing memorized...
Newer checklists have boldface on them for many aircraft. This was a change that came about from best practices by professional crews who have had that for a long time. The boldface items are *required* to be committed to memory and the pro crews are tested on it. You'll talk to folks who hated "memorizing the boldface".
I've seen a pro crew from the jumpseat rattle off a call-and-response checklist completely from memory though -- when no one was looking, but the CVR was recording.
When you've done that checklist 10,000 times, you tend to have it pretty well memorized, and can change crew members out and not even notice if the other person in the cockpit is actually reading from the thing, apparently.
Few of us lowly Private aviators doing it for fun are getting to read ours quite that often, so I definitely recommend having it out, organized, available and use it in front of a DE... unless your instructor knows something about your DE that we here don't!