Yes and no. You'll be barraged with a bunch of shit that you don't understand like innocents on items - items with "Manager" or "Gladiator" or whatever on them - but immediate comprehension isn't ever required. The story mode is 30+ hours of sustained acclimation, after which the postgame presents a host of challenges that'll require more investment into the game's mechanics.
I've played 3, 4, D2 and 5, and for all except possibly D2 - and I guess 5 is yet to be determined - there's a couple ways to go about progressing, and they'll all work, whether you understand what you're doing or not. The first is to just wing it, and it works. I don't think there's really an easy way to fuck up your characters, but youcanbe grossly inefficient. The second is to follow some sort of maximization guide, which is also quite fun but there'll be classes you never try because you weren't told to experiment. This happened to me in 3 and 4, and probably would have happened in D2 except I couldn't find a decent guide and I enjoyed it way more as a consequence.
5 is so new that you'll resort to option 2, and it's fun as hell. It does have a more robust tutorial system than any prior game, also.
In short, you'll probably be lost, but you'll not be fucked. At all. The only drawback to starting with 5 is that if you fall in love with it, it's likely gonna be hard to go back to earlier games, possibly excepting D2. I'd start there anyway, though. I began Disgaea only a few months ago, and put like 80-100 hours into 3 and 4 and 30 into D2, but my playtime was abbreviated because I had my eyes on 5. So this'll be the first one that I've completely invested in.