Well. Not really, I mean you can watch the original series and get kinda gist for the older characters. They do focus on Snake, Spike, Joey, & Catlian in the beginning because they were characters in the original show. Correct me if I'm wrong but I think the show starts during the year of 2001 and the original Degrassi characters are having their 10 year reunion and I'm guessing they graduated sometime in 1991. They really kinda steer away from them after a while. If you kinda want your back story for those characters and how Emma was born and what not, I suggest you watch the original show.
For instance, in one of the episodes Snake is feeling kinda depressed, for reasons I wont say since I don't know if you watched the show or this particular episode. But back to what I was saying, Snake was depressed about something going on in his life. He meets up with an old buddy, I'm not too sure if he was in the original show, because I never watched it really. but from the way it seems is the guy I'm referring to had an incident in the show or around the show's time that he's referring to that Snake clearly knows about. Also, the whole mystery of what happened to Emma's dad may reflect on what happened in the real show. There is an episode in the newer show revolving around Emma going on a hunt and search kind of deal to find out what happened to her REAL father.
All in all, the original show really just focuses on the people living at that time obviously. You get to see where Joey, Snake, Spike and what not came from. The newer show is really about the kids, hence its called the NEXT generation. I started watching the next generation without even knowing about the original show. I didn't realize until somewhere during the process of watching the show that there was an original show. One of my Science teachers noticed I was a fan of the Next Generation and she made mention she was a fan of the original. I'm like "woah there is an original??" so ...if you want back stories on the adults in the show. Go for it. Though now the show's really moved on from the 80's degrassi people because now the 2000s degrassi people are all old and should be out of college now lol.
In my honest opinion, the show should kinda be over now? or just create a newer one? I don't see why they should focus on all these newer kids and re-hash the same old story lines time and time again. Oh well, I guess that's the point of the show. It's kind of humorous to see every incident happen, that you hear about maybe once every couple of years (like school shootings and people getting stabbed) all to the same clutter of people within a limited amount of time.
So if you really want back story, go ahead! you're more than welcome to. If not, you won't be lost at all. You just get to see really where Emma came from and the stories about the older crowd. Enjoy!