No. I finished it around 3 days ago and immediately started D2, and I regret it. It's not a direct follow up, so imagine the disappointment of realizing that nothing from the first game is even touched upon in D2, at least not in the first 6 hours I've played thus far.
Different cast that's really hard to get into, different setting, and crazy amped up difficulty.
To put it in perspective, when I played the first game, I played it all the way until the start of the second trial without taking a single break. I had to plug in my Vita into the charger multiple times, but that's how much I was excited. However, with the second time, I must have taken 3 or 4 breaks before the first trial even started, and I stopped playing and put it to the side while in the middle of the first trial.
Nothing against the game, and I have no doubt that it will be better than the first game, but I was burnt out by the end of Trigger Happy Havoc, and the extremely slow start of the second game only made me bored and hesitant.
I recommend starting a different game, play it for a while, and once you find yourself less excited about Danganronpa, start the second one.