No, he was definitely not enraged when he turned SS2 against Kibito. He had calmed down at that point and even had the sunglasses gag and showed embarrassment.
I don't think the dialogue implies that Gohan's inaccessible power was SS2. It was just his regular "get angry, get powa" boost, especially given Vegeta's quote:
Vegeta: “Unfortunately, it seems he got carried away in peace and didn’t do any significant training. Our powers are higher than his now…Though I suppose there’s no telling what would happen if he snapped and went into a frenzy… ”
That leads me to believe Gohan's rage power isn't simply Super Saiyan 2, or they would definitely know what to expect from his going into a frenzy. Vegeta also doesn't mention that Gohan still has his "Super Saiyan beyond Super Saiyan" up his sleeve, acting as though his anger is the only thing left for him to accomplish.
Furthermore, the fact that he was able to transform into a Super Saiyan 2 at all rules out that being his anger power to me. We get this quote later:
Gohan: “I-I am angry…! I’m angry, but…[it’s not] like it was ba-back then…”
Suggesting Gohan isn't lacking in anger, but being angry just doesn't have the effect it did when Gohan was a child. Which goes against him using his anger to fuel his Super Saiyan 2 state at the tournament.
I think it's plausible for Gohan to be a Super Saiyan 1, however I don't think it's plausible for him to be unable to turn into a Super Saiyan 2 because he lacks rage or that he only turned into a Super Saiyan 2 at the tournament because he was angry about Videl.