Is ending up in hell at some point in time inevitable for those beings who are not Stream-Entrants? I have seen this a few times in various places, although I haven't read it in any suttas, but I am guessing there might be some that talk about this.
The 4th jhāna brahma and above have a long enough age to meet more than 1 buddha, they are not going to hell until they die. So buddha can't say "If you do not enlighten by my teaching, you are going to hell soon".

However, most being are going to hell, included dead brahma, by Sutta. Saṃ. Ma. Āmakadhaññapeyyāle:


  "In the same way, monks, few are the beings who, on passing away from
  the human realm, are reborn among human beings. Far more are the
  beings who, on passing away from the human realm, are reborn in the
  animal womb... in the domain of the hungry ghosts.
  
  ... "In the same way, monks, few are the beings who, on passing away
  from the human realm, are reborn among devas. Far more are the beings
  who, on passing away from the human realm, are reborn in hell... in
  the animal womb... in the domain of the hungry ghosts.
  
  ... "In the same way, monks, few are the beings who, on passing away
  from the deva realm, are reborn among devas. Far more are the beings
  who, on passing away from the deva realm, are reborn in hell... in the
  animal womb... in the domain of the hungry ghosts.
  
  ... "In the same way, monks, few are the beings who, on passing away
  from the deva realm, are reborn among human beings. Far more are the
  beings who, on passing away from the deva realm, are reborn in hell...
  in the animal womb... in the domain of the hungry ghosts.
  
  "Therefore your duty is the contemplation, 'This is stress... This is
  the origination of stress... This is the cessation of stress.' Your
  duty is the contemplation, 'This is the path of practice leading to
  the cessation of stress.'"


Hurry up.