I have some/little experience with felted flat roofs.
Neither do I know to what extent the board/decking is drooping but,
dependent upon age, it does suggest they are a chipboard form. If so,
you are right to avoid putting any extra weight on the surface; even to
the extent of chancing walking on the supporting rafters. Though, you
could use a couple of planks across the rafting.
If the droop is pronounced, any water collection will accelerate the
process due to the weight; discounting the effects of any frost. In
which case, paint will not prevent further drooping and any subsequent
tearing.
The decking is, more likely, to be subject to the changes in internal
atmosphere rather than the external.
Should you decide upon having the roof replaced consider marine ply else
if applicable, converted to a slate/tile roof.
....Ray.
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