No. The rules are on p 82 of the DMG. If a character is dropped below 0 hp (optionally, below -3) s/he dies. At zero (optionally, between 0 and -3 inclusive) s/he is unconscious, losing 1 hp per rd, and dies of this hp loss drops him/her to -10. If the bleeding is staunched and s/he has hp restored, s/he is still comatose for 10 to 60 minutes and requires a week of rest.Wasn't 0hp just dead in 1st Edition?
As presented, it was not an option; the only option was whether death occurs if dropped below zero, or if dropped below -3. (Like [MENTION=6799753]lowkey13[/MENTION] posted.)Another 1e DMG option: you could let PCs survive down to -10, but they required a week of bedrest to recover, even if fully healed up magically. Most every DM I knew back then used that option and/or other home-brew or Len Lakofka variants to make 1st level a little more survivable.
In Unearthed Arcana there was a 3rd level cleric spell, Death's Door, that alleviated the need for the week of rest. It was very popular in my AD&D game.