If the hay has been cut and it is rained on then the nutrients leach out of it, so yes the hay will be of a lower quality.
If the hay cannot be cut before the hay has gone to seed then it can only be sold as Meadow Hay, which is of a lower nutritional value to Seed Hay anyway.
If the hay does not grow to its usual height and denseness then there will be a shortage.
Mine has been flattened by the rain so many times it is likely to be a bit mildewed and poor quality. There will be lots of it though - if we can ever get it made!!