Ryan went through a period of not napping at home for several weeks and it DROVE ME INSANE. This was early in my pregnancy, when I was crazy exhausted and just felt all-around awful. He would still nap at preschool, where he goes three days a week, so I got that break...but I was working (I am a writer and work at home) so it wasn't like I was totally "free," kwim?
Then I discovered that if I took Ryan out either all morning and then for lunch, OR if I took him out for a couple of random errands after lunch, he'd fall asleep in the car around 1:30/2 p.m. So lo and behold, that is my strategic way of getting him to nap! He NEVER transferred to bed when he was an infant, but now I bring him inside and he curls up on the sofa and is out for about 1 1/2 to 2 hours, sometimes longer! Whew! He goes to bed between 8:30 and 9 p.m., and gets up around 6:45/7 a.m.
So...in answer to your question, Ryan obviously still needs his nap, though even when he DIDN'T have it several months ago, he'd be OK (not super-cranky most days).
I love the idea of "quiet time" in his room even if he doesn't nap, and hopefully once my new baby comes, I'll be able to institute that a little if I can't get all of us out of the house for the strategic nap!
Good luck!