It would seem that his fate, at the end of HTTYD2, was left intentionally ambiguous. The original script doesn't say anything about him other than mentioning that he follows his bewilderbeast into the ocean with a splash and isn't seen again (although his mount makes an appearance a few hours later)
Overwhelmed and overpowered, the Bewilderbeast yields to the new alpha and heeds Toothless' command, retreating into the sea in an explosive splash.
The Berkians CHEER in victory!
As the smoke clears, Hiccup and Toothless see nothing but bubbles on the waves to mark their disappearance. No sign of the Bewilderbeast... or Drago..
... [shortly later]
All of the dragons -- Berk's, Valka's, even Drago's -- land around Toothless. Cloudjumper bows to Toothless, starting a wave of bows, acknowledging their new alpha.
That all being said, his return was extensively discussed (and even scripted) by the makers of HTTYD3. Ultimately it was cut out and another version of the film was finalised, which leaves Drago back in 'Hollywood limbo', trapped between life and death.
...so in early drafts of Dragon 3 we did focus on the return of Drago.
I had always intended to give more dimension to the character by
showing a redeemed version of him by the end of Dragon 3
Midway through the development of Dragon 3 I was asked to come up with
a fresher take that wasn't dependent upon Dragon 2 because it was
starting to feel like "Dragon 2, Part II", so very wisely Steven
Spielberg had said to me "the redemption story of Drago requires so
much screen time that you don't have in order to really sell it
properly and you would do yourself you know a disservice to try to
force it in"