Maybe. Although, Elite will have 2 years of content updates, tweaks and fixes. I would Imagine by the time Star Citizen is close to release Elite will be in full swing with quite a large player base and a lot of people will have mastered the controls of the ships by then. After playing a game like Elite the arcade type of game just kind of loses it's appeal - at least for me. I mean they are fun to jump on and play every now and then but you can only do so much in those types of games. Whereas Elite will be like an alternate life with an entire universe to explore.
Like everything SC will be newer, the next big thing. So people will 'upgrade' maybe you could say.
I imagine lots of people who love elite will also want to play SC, me being one, I'll probably go back and forth, and I'm guessing in the end I will probably end up going back to full time Elite.
Elite has the advantage of being first, people who cant wait for SC may take up elite, elite probably would have been more popular now if there was no SC and people didnt divide between the two.
It could be like PES and FIFA used to be 10 year ago, when PES challenged FIFA despite FIFA having the bigger budget, you get a group that are loyal to FIFA and a Group that are loyal to PES.
Theres no doubt that SC will be the most successful, but that certainly doesnt mean it will be the better game.
I think Elite will have a huge boost once reviews and word of mouth start spreading.