No and why would you think so ?
Barbarian intimidate checks are usually of low Charisma DC. They dont get advantage though.
Personally I would have given them high Strength DC instead.
If you want advantage for Intimidate, you may consider taking steps to get the Thaumaturgy cantrip:
- taking a level of Cleric
- playing as Zariel Tiefling
- playing as the new patch 8 subclass Giant
- or talking the Magic Initiate: Cleric feat.
https://bg3.wiki/wiki/Thaumaturgy