No, with INT 1 you wouldn't even be able to talk or comprehend language. Even wild animals like wolves have INT 3. 4 is the bare minimum INT needed to be considered sapient.
Even at that point though you'd be way too stupid to be attractive to the average goblin. Or even a very stupid goblin. The average goblin statblock in 5e gives them 10 INT, which means they're about on-par with the average human. It is their WIS and CHA that are lacking at 8 each. This is likely because while goblins aren't educated they are pretty good at devising traps.
INT 4-5 seems what you're looking for, and that'd put you on par with the ogres we see in the game.
At which point we'd also need to consider the game balance of being able to drop your INT to 4 and then find a headband that gives you INT 18 fairly early in the game.
Personally if we're going to have an "idiot" playthrough I'd rather it be a personality tag than tied to our stats. You can be an idiot wizard who's great at math and spells but utter crap at paying attention to the world around him and constantly makes heinously bad decisions.
The stone has no intelligence, while the squirrel has 3.
And who has intelligence 1?
Yes, I think 4-5 intelligence would be enough for such a passage. But I think it's not right to be "great at math and spells" with intelligence 4. The whole fun of this walkthrough is that you are an idiot, and everyone perceives you as an idiot with a dead brain. Even the goblin Sazza looks as a more wiser and smarter.
