Not exactly. Portable CD players were still selling in droves, and my bro was still using a sony discman when i got my first iPod.
Actually, I remember when the iPod came out - it kinda sat there, not unlike how the Apple TV did for the first year or so it was on the market. The initial ads were embarrassingly corny, and one tech mag even called it the new pocket protector.
Let's not rewrite history. I bought my first portable CD in 1986. That's 1986!, 15 years prior to the iPod. CD players were merely a replacement for the cassette walkman, which was a reinvention of portable audio. But by the mid 90s the concept of portable audio wore stale and thin judging by the # of people one would see in public with a portable CD player vs. when the cassette walkman became a hit.
The clunky nature of the players + the fact you had to carry around CDs made people leave them at home once the novelty wore off. By the late 90s you hardly saw anyone at a fitness club, or on a plane, train, with a portable CD player... places they were once common place. In Europe and Japan Sony's MiniDisk tried to pick up the slack and was marginally popular, but it never took off in the U.S.
The MP3 format popped up in the mid 90s and MP3 players soon followed, but were mostly only adopted by the gadget geek class, not gen public. Their cost:storage ratio and the fact the concept hadn't yet connected with the techno/computer-shy gen public kept the category at a slow growth rate.
Enter Apple's iPod. Yes, it was initially mocked (I remember the forum chatter here the day it was released. Negative (and proved to be wrong) as usual). But 5,000 songs on something the size of deck of cards
was exciting and compelling. Sales were steady for a Mac-only device, and when the 2nd gen came out w/ Windows support there were lines on launch day at Apple Stores across the U.S.. Apple's digital music revolution was in full swing.
It wasn't too long before you once again saw people on the street, the gym, planes, etc with a portable audio device... an iPod. Then of course, the iTunes Music Store completed the new concept of portable digital music. That is what is called reinventing a category. It wasn't much longer when every electronic company in the world was trying to copy Apple's model.
To come full circle here... yes, lots of people owned portable CD players in 2001. But not many people actually used them on a daily basis. Same thing can be said for watches today. But Pebble is already showing that the watch concept can be modernized to be relevant again. Apple can refine it even more, just like it did with portable audio because that is its expertise.