So you want to put this hayland into pasture... do you know what forages are actually growing in there, if none of it is bermuda, or even some type of bermuda as greybeard pointed out?
What you need to know is that typically the number of cuts for hay doesn't exactly reflect how much grazing can be done on there. That in itself tells me nothing. It doesn't tell me average forage yield, or how many bales they got off that per acre (and how heavy those bales were), and the resulting quality.
The number of times you can come back to a grazed area depends on moisture, temperature, and recovery period needed based on how much forage was eaten. If there's lack of moisture and cooler temperatures, more time is needed for plants to recover. If forage was heavily utilized (like, if you had animals in there graze quite close to the ground), then it will take longer to recover. Animals aren't going to be grazing as close to the ground or be as efficient at "harvesting" what's there like a hay outfit is.
And yes you can graze this land without cutting. The only time you will need to cut is if you don't have enough grazing power from your animals that the plants get way ahead of you, no matter what grazing system used.
For hay cutting, the standard rule of thumb is typically when plants have just began to head out, or legumes are just starting to flower (like 10% bloom) to get hay that is the best quality. But this can change with different plants. Sainfoin, for example, can be cut at a later bloom (50 to 100% bloom) than legumes like clover or alfalfa.
