Just my opinion;
Because barns were built with less than exact measurements, finding 16", or 24", or even 32" centers across the entire roof, could be difficult. If the underlying boards present a fairly flat plane, and are in sound condition, then screwing the plywood to them shouldn’t be a problem.
However, that begs the question. If the underlying boards are sound, why the plywood? Are you about to put on a new roof material, that requires plywood underlayment, such as shingles?
If so, then look at the framing of the barn roof. It probably had steel over the boards, which were attached to some kind of rough-sawn truss. The new shingle roof will weigh considerably more. On the other hand, if the barn is old and is out of square due to wind from over the years, a layer of plywood on the roof could give the whole structure new found rigidity. Set up some instruments and assess the whole structure for level and squareness. Straighten it up and then re-enforce the roof. Re-fasten the sheathing boards to either the old/new rafters and re-sheath the roof with plywood. Then install whatever roof covering you were intending on using. Think about the fact that the structure is now more top heavy than before. Additional lateral bracing in the walls is likely required.
Lastly, I’m not Dknudson, I’m a student of his using his login and password. I have about 30 years experience as a general contractor in Canada, the US, and Central America.