Conjecture. No way to say that with certainty for every conversion. With most such conversions that probably is true, but it is not an absolute.
I know of a TDI powered formerly V6 Toyota 4x4 mini-truck. His mileage about doubled while the power remained the same. No idea of his conversion cost, but since he all of the work himself I'll venture that his pay-off point isn't too far in the future. Factor in that he's running it on mostly free to him bio-diesel and he's probably passed the pay-off point.
I wouldn't do it to save money. I'd do it for range, how far can I go btwn fill-ups w/o building some ginormous fuel tank?
As a long term diesel owner (had one on and off since '95) around these parts diesel fuel's price runs about equal to mid-grade gasoline. When there is a price spike diesel lags gasoline, but eventually over-shoots it before slowly settling back down to about the price of mid-grade again.