If I were to send a 3 intimidate character on a power challenge at an opponent, and they block with a strength 1 power character with crown regent, the result of the challenge is opposed, correct?

(the attacker would win the challenge still (3 to 3) but no unopposed)

Yes, that's all correct. Intimidate does not remove the character from the challenge and the title only cares that you have a participating character, not that that character's strength counts during the challenge resolution.