Others can probably answer better than I, but I doubt it, or at least see no correlation. There are still 18 tees, greens, and fairways to apply cultural practices to, no matter what the design.
Basically, you can ease maintenance by:
Reducing acres of turf (minimalists seem to be into expanding fairways to huge proportions, although the do reduce the number of different cuts at the same time)
Reducing size and complexity of bunker maintenance, but I think the jagged edge probably takes a lot of time to keep right.
Make the fewest number of steep slopes (i.e., mounds) to keep mowing production high, and I think most minimalist designs would shine here. Less steep slopes might reduce water consumption, too, perhaps saving cost if they pay for water.
IF they eliminated cart paths, there might be more labor roping, re-sodding, etc. (Might)
Overall, it is probably a wash, but each case would be different. We have often tried to quantify savings, but so often, the budget ends up the same as it was, but with emphasis on different areas with the same amount of funds.