There's a bunch of questions here, and each needs an individual answer. In order, I'd have to say;
No. It's a bit like paying your Visa bill with your Mastercard. You've traded one set of problems for another, but you've still got problems of some sort. I've used a lot of different moly processes during testing and evaluations, and for my own personal shooting, I won't even consider them. Not worth it.
Yes and No. Velocity is a bit of a wash, here. Using moly coated bullets reduces pressure, with in turn reduces velocity. Reduced pressures mean you can generally add more powder to get the velocity back, but we're sort of back to the Visa/Mastercard situation.
Accuracy . . . yes, it may affect accuracy, and no, it doesn't "improve" it. I ran an awful lot of very rigidly controlled tests with nearly two dozen different coatings, and a lot of them seriously degraded accuracy. The best ones (the ones that are still available and popular today) didn't hurt accuracy at all, but none of them improved after coating. Yes, the bullets were tested against others from the same lot, and with all other variables kept to an absolute minimum. Several of the others seriously degraded accuracy.
The other drawbacks are that it's time consuming and messy to deal with, and the fact that the barrel will need to be "re-seasoned" after every cleaning, before the accuracy settles back down and the gun starts shooting normally again.
There's some folks that like this stuff, and others who don't. Just comes down to which set of problems you'd rather deal with, the Visa or the Mastercard.