No.
No it won't. There will always be people playing Destiny much like people still play WoW. It wont just fade away into obscurity of that I'm 100% certain (looking at you fanbois).
BUT.......
Anthem, even if it is by greedy EA and buggy as AF atm, will still attract many Destiny players to it. Why? Because it's something new to do. Many players are fatigued by the Destiny franchise....shooting the same freekin enemies...doing the same activities each week....waiting for new content half the time. Bungie have lost a lot of goodwill amongst the player base (for good reason) so many of us will go eventually. If not to Anthem then perhaps to Cyberpunk or Borderlands 3 when it drops. Bungie are facing an uphill battle in 2019 make no mistake. Players will come...and go...but the golden days of Destiny are numbered. Perhaps if Bungie were more engaged with the community and more transparent with thier plans, changes, and so on...more of us would stay but they've always been terrible at that. I enjoyed Destiny, had my fun (for the most of it) but I can't see myself sticking around for another 4 or 5 years. And for those of you who do......great....hope you continue to have fun. Glad you still find Destiny worth your time and investment....certainly don't hold that against you. Just know that your player base is likely to dwindle fairly dramatically this year.
(Edit: Wow...a lot of great replies! Unexpected but thanks everyone.)
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Too be honest, Anthem seemed too much like Warframe and I never payed attention to what was going on in Warframe. So I expect Anthem to die within 2 months.