@Henroo I don't think so. It's not something I've needed to know for a long time, but I think any points get you in.
From the wiki:
"All Tournament Points gathered in Provinces, by you and your fellows, are combined! At each checkpoint you reach, you open a Chest and more rewards you and your fellows will get at the end of the Tournament! As you progress through the Chests you will even get
Royal Restoration Spells, which are useful for upgrading Building Sets and Event Buildings and a
Blueprint for the final chest, which is very useful to upgrade your Magic Residences and Magic Workshops.
Remember: You have to earn at least 1 Tournament Point to get any rewards from the Tournament!"
That doesn't explicitly say 1 point gets you everything... but I think that's the intent.