Fallout – Help with the quest “Oh the Papa!”

No.

There is a clearly delineated "Point of No Return", whereby setting out upon the final quest requires you to explicitly tell an NPC that you'd like to do so, from which point you can no longer explore the Wasteland, and once completed, the game has an ending, from which point, you can't continue playing. While this point is fairly obviously telegraphed, if you happen to not see it coming, the final quest involves returning to the Hoover Dam, after completing quests involving President Kimball.

It only adds +9 radiation immediately when you eat it, then it gives you 5 HPs over 5 secods, 1HP every second.

You have to note that the (5s) description is only part of the HP +1 effect, not the Rad effect.