Yes, but nobody ever heard of it until it was mentioned as an also-ran in Wikipedia's article about DAPs. (That said, I did just finish updating my prior comment to reflect that the iPod wasn't the first HDD-based player to market, but I think it is still fair to say it was the first one that mattered.)
Kids had MP3 players before the iPod. I remember them in high school and yes they were a known music player alternative to CDs. The iPod landed with a unified marketing campaign that promoted itself as a music device vs an MP3 player. The marketing campaign was sleek and different.
But those flash based MP3 players didn't have much storage (certainly not several GB), and typically had a terrible UI, if they could handle meta data (song, artist, album, genre) at all.
Before the iPod, a DAP was an alternative to a Discman. After, it was the other way around - at first for rich kids whose families could afford the requisite Macs for iTunes, but once iTunes for Windows came out, a Discman was what you had if you were poor.
Even if they weren't nearly as ubiquitous as they would become, people absolutely had heard of DAPs before the iPod came out. And, like the iPhone, it took 2 or 3 generations before it was obvious to a lot of people that this was something different--in part because of the ecosystem.
