Would it make me happier? I say yes, mainly because I already have a plan for it.
I'll take "filthy rich" to mean at least 15x more money than you would need to be merely "comfortable" for the rest of your life, something like $50 million, in 2013 dollars
On the well-known phenomenon of lottery winners ending miserable/bankrupt or both: I don't think that being poor per se prior to hitting the jackpot is the reason why that happens. I think it's because lottery playing itself is an indicator of the very mindset that keeps these people poor, and renders them vulnerable to the kinds of problems seen among so many winners afterwards. Ever heard the saying that "lotteries are a tax on people who are bad at math?" By definition, lottery winners are drawn from the pool of people who think playing lotteries is a good idea.
On relationships changing. Oh yes, that happens. I think I have an advantage in this department, however. In addition to being discreet in setting my affairs up after the win (lawyer and accountant get the phone calls, right after my mom), I'm not morally vulnerable to any sort of altruism. Here I don't mean benevolence; there are charities I would support, and family goes without saying too. I mean the idea that there exists some sort of unchosen obligation or duty to the "less fortunate". Anyone drops even a *hint* of entitlement mentality, and that's it; one strike and you're out. Better off without, I say; with friends like that...
Beyond that, the help I give would be at my initiative, and would often be clandestine (an earlier poster's idea of paying off someone's debt behind their back appeals to me a lot.) I am inclined to agree that there can be a lot of joy in helping others, but my reward is in the helping and in the results... especially when a person is moved by anonymous generosity to look at their fellow man more optimistically; when you don't know who in a crowd gave you a hand, you're more inclined to extend goodwill to anyone in that crowd. A nice multiplier effect there, I'd say.
Being rich can make you paranoid, yes... there *are* lots of people out for your wealth, some of them the people whose job it's supposed to be to protect you from such things. But in addition to the legal protections, there's ways of having backups within backups. I also think that while I might not need a job anymore, one should always be doing something... working, studying, learning, and volunteering too. There's no shortage of things to do in the world, and a living mind is an active one.
In the same way that you might have a rags-to-riches plan like I'm talking about here, have a riches-to-rags plan too, a sort of financial Condition Yellow. If I remain capable of living well without the money, the fear of losing it all just doesn't have the same sting, and having backups within backups helps too.
So I'd say, absolutely it would make me happier. Not only because I am confident in my plans for how I'd handle it, but there's these specific reasons: I would be able to get the best of the best treatment for my wife should her cancer ever come back... and in the meantime, it would make it easier to get the most out of the "extra time" I'm having with her right now.
Money is a means, not an end. It helps to have ends in life should you suddenly come into a lot of means.